Researcher Database

Hitoshi Furuhata
Faculty of Science Mathematics Mathematics
Associate Professor

Researcher Profile and Settings


  • Faculty of Science Mathematics Mathematics

Job Title

  • Associate Professor


J-Global ID

Research Interests

  • 微分幾何学   Differential Geometry   

Research Areas

  • Natural sciences / Geometry

Academic & Professional Experience

  • 1999 - 2007 北海道大学大学院理学研究科数学専攻 講師
  • 1999 - 2007 Lecturer
  • 2007 - 北海道大学大学院理学研究院数学部門 助教授
  • 2007 - Associate Professor
  • 1996 - 1999 Tohoku University Graduate School of Information Sciences
  • 1996 - 1999 Research Associate
  • 1995 - 1996 日本学術振興会 (東北大学) 日本学術振興会特別研究員
  • 1995 - 1996 Postdoctoral Fellowships of Japan Society for the Promotion of Science

Association Memberships

  • 日本数学会   Mathematical Society of Japan   

Research Activities

Published Papers

  • Naoto Satoh, Hitoshi Furuhata, Izumi Hasegawa, Toshiyuki Nakane, Yukihiko Okuyama, Kimitake Sato, Mohammad Hasan Shahid, Aliya Naaz Siddiqui
    Information Geometry 2511-2481 2020/09/04 [Refereed][Not invited]
  • FUJIOKA Atsushi, FURUHATA Hitoshi
    Bull. Braz. Math. Soc., NS. 50 (1) 291 - 313 2019 [Refereed][Not invited]
  • FUJIOKA Atsushi, FURUHATA Hitoshi
    An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 64 343 - 355 2018 [Refereed][Not invited]
  • Hitoshi Furuhata, Izumi Hasegawa, Yukihiko Okuyama, Kimitake Sato
    Journal of Geometry 108 (3) 1175 - 1191 1420-8997 2017/12/01 [Refereed][Not invited]
    A notion of a Kenmotsu statistical manifold is introduced, which is locally obtained as the warped product of a holomorphic statistical manifold and a line. A statistical manifold is a Riemannian manifold equipped with a torsion-free affine connection satisfying the Codazzi equation. It can be considered as being in information geometry, Hessian geometry and various submanifold theory. On the other hand, a Kenmotsu manifold is in a meaningful class of almost contact metric manifolds. In this paper, we construct a suitable statistical structure on it. Although the notion of the warped product of Riemannian manifolds is well known, the one for statistical manifolds is not established. We consider it in general, and study the statistical sectional curvature of the warped product of two statistical manifolds. We show that a Kenmotsu statistical manifold of constant ϕ-sectional curvature is constructed from a special Kähler manifold, which is an important example of holomorphic statistical manifold. A Sasakian statistical manifold is also studied from the viewpoint of the warped product of statistical manifolds.
  • Hitoshi Furuhata, Izumi Hasegawa, Yukihiko Okuyama, Kimitake Sato, Mohammad Hasan Shahid
    JOURNAL OF GEOMETRY AND PHYSICS 117 179 - 186 0393-0440 2017/07 [Refereed][Not invited]
    A notion of Sasakian statistical structure is introduced. The condition for a real hypersurface in a holomorphic statistical manifold to admit such a structure is given. (C) 2017 Elsevier B.V. All rights reserved.
  • Hitoshi Furuhata
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10589 179 - 185 1611-3349 2017 [Refereed][Not invited]
    This article is a digest of [2, 3] with additional remarks on invariant submanifolds of Sasakian statistical manifolds.
  • Hitoshi Furuhata, Izumi Hasegawa
    Geometry of Cauchy-Riemann Submanifolds 179 - 215 2016/01/01 [Refereed][Invited]
    A statistical manifold is a smooth manifold equipped with a pair of a Riemannian metric and a torsion-free affine connection satisfying the Codazzi equation. We naturally have various dualistic geometric objects on it. In this article, the basics for statistical submanifolds in holomorphic statistical manifolds are given. We define the sectional curvature for a statistical structure, and study CR-submanifolds in a holomorphic statistical manifold of constant holomorphic sectional curvature. We prove that this sectional curvature of such a space vanishes if it admits a totally umbilical and a dual-totally umbilical generic submanifolds. Furthermore, we show that a Lagrangian submanifold is of constant sectional curvature if the statistical shape operator and its dual operator commute. Similarly, we generalize several theorems in the classical CR-submanifold theory.
  • Projective surfaces and pre-normalized Blaschke immersions of codimension two
    FUJIOKA Atsushi, FURUHATA Hitoshi, SASAKI Takeshi
    Int. Electron. J. Geom. 9 100 - 110 2016 [Refereed][Not invited]
  • Atsushi Fujioka, Hitoshi Furuhata, Takeshi Sasaki
    Journal of Geometry 105 (1) 87 - 102 0047-2468 2014/04 [Refereed][Not invited]
    Centroaffine minimal surfaces are considered as an interesting class of surfaces from the viewpoint of not only variational problems in centroaffine differential geometry but also integrable systems. Typical examples of centroaffine minimal surfaces are proper affine spheres centered at the origin when we regard them as centroaffine surfaces. On the other hand, the study of projective minimal surfaces has a long history in projective differential geometry. Typical examples of projective minimal surfaces are proper affine spheres again, and so-called Demoulin surfaces or Godeaux-Rozet surfaces. In this paper, we shall regard centroaffine surfaces as projective surfaces and study projective minimality of centroaffine minimal surfaces. Using the fact that any centroaffine minimal surfaces have a one-parameter family of deformation known as associated surfaces, we shall give a classification of indefinite centroaffine minimal surfaces whose associated surfaces are all projective minimal, which includes centroaffine surfaces with vanishing Tchebychev operator and those found by the first author before. We shall also show that any indefinite centroaffine minimal surface whose associated surfaces are all Godeaux-Rozet surfaces is a proper affine sphere. © 2013 Springer Basel.
  • Hitoshi Furuhata, Takashi Kurose
    TOHOKU MATHEMATICAL JOURNAL 65 (1) 31 - 42 0040-8735 2013/03 [Refereed][Not invited]
    We classify the maximal Hessian manifolds of constant Hessaian sectional curvature nonpositive.
    J. Van der Veken, I. Van de Woestyne, L. Verstraelen, L. Vrancken (eds.), Pure and Applied Differential Geometry - PADGE 2012 In Memory of Franki Dillen, Shaker Verlag GmbH, Germany 136 - 142 0945-0882 2013 [Refereed][Invited]
  • Hitoshi Furuhata
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 29 S86 - S90 0926-2245 2011/08 [Refereed][Not invited]
    A rigidity theorem for a statistical hypersurface of Hesse-Einstein type is given. (C) 2011 Elsevier B.V. All rights reserved.
  • Hitoshi Furuhata
    DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS 27 (3) 420 - 429 0926-2245 2009/06 [Refereed][Not invited]
    The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given as a first step of the statistical submanifold theory. A complex version of the notion of statistical structures is also introduced. (C) 2008 Elsevier B.V. All rights reserved.
  • Hitoshi Furuhata, Luc Vrancken
    Results in Mathematics 49 (3-4) 201 - 217 1422-6383 2006/12 [Refereed][Not invited]
    We study the center map of an equiaffine immersion which is introduced using the equiaffine support function. The center map is a constant map if and only if the hypersurface is an equiaffine sphere. We investigate those immersions for which the center map is affine congruent with the original hypersurface. In terms of centroaffine geometry, we show that such hypersurfaces provide examples of hypersurfaces with vanishing centroaffine Tchebychev operator. We also characterize them in equiaffine differential geometry using a curvature condition involving the covariant derivative of the shape operator. From both approaches, assuming the dimension is 2 and the surface is definite, a complete classification follows. © 2006 Birkhäuser-Verlag Basel.
  • H Furuhata, T Kurose
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN 9 (4) 573 - 587 1370-1444 2002/10 [Refereed][Not invited]
    We explicitly determine the self-dual centroaffine surfaces of codimension two with constant affine mean curvature and indefinite affine fundamental form by giving representation formulas.
  • Codazzi structures induced by minimal affine immersions
    FURUHATA Hitoshi
    Banach Center Publ. 57 17 - 19 2002 [Refereed][Not invited]
  • H Furuhata
    BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN 7 (1) 125 - 134 1370-1444 2000/01 [Refereed][Not invited]
    Minimal equi-centroaffine immersions of codimension two are characterized as solutions of a certain variational problem. We determine the moduli space of such immersions of R-2 into R-4 whose induced connection and affine fundamental form coincide with the ones of the Clifford torus.
  • A conformal gauge invariant functional for Weyl structures and the first variation formula
    ICHIYAMA Toshiyuki, FURUHATA Hitoshi, URAKAWA Hajime
    Tsukuba Math. J. 23 551 - 564 1999 [Refereed][Not invited]
  • Hitoshi Furuhata
    Journal of Geometry 65 (1-2) 111 - 116 1420-8997 1999 [Refereed][Not invited]
    We give an intrinsic characterization of isometric pluriharmonic immersions of Kahler manifolds into semi-Euclidean spaces with real codimension one which is a generalization of the Ricci-Curbastro theorem. © Birkhäuser Verlag, 1999.
  • Holomorphic centroaffine immersions and the Lelieuvre correspondence
    FURUHATA Hitoshi, MATSUZOE Hiroshi
    Result. Math. 33 294 - 305 1998 [Refereed][Not invited]
  • FURUHATA Hitoshi, MATSUZOE Hiroshi, URAKAWA Hajime
    Interdiscip. Inform. Sci. 4 (2) 125 - 127 1998 [Refereed][Not invited]
  • H Furuhata
    GEOMETRIAE DEDICATA 66 (3) 303 - 311 0046-5755 1997/07 [Refereed][Not invited]
    We prove a cylinder theorem for isometric pluriharmonic immersions of complete Kahler manifolds into semi-Euclidean spaces under an assumption concerning the index of relative nullity.
  • H Furuhata
    PACIFIC JOURNAL OF MATHEMATICS 176 (1) 1 - 14 0030-8730 1996/11 [Refereed][Not invited]
    We classify isometric pluriharmonic immersions of a Kahler manifold into an indefinite Euclidean space. The moduli space of such immersions is explicitly constructed in terms of complex matrices. Some examples of these immersions are also given.
  • Isometric Pluriharmonic Immersions of Kaehler Manifolds into Semi-Euclidean Spaces
    FURUHATA Hitoshi
    Tohoku Math. Publ. 1 1 - 70 1995 [Refereed][Not invited]
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY 26 487 - 496 0024-6093 1994/09 [Refereed][Not invited]
    A classification of isometric minimal immersions of Kahler manifolds into Euclidean spaces is given, which is a generalization of the Calabi-Lawson theory concerning minimal surfaces. Moreover, we explicitly construct a nonholomorphic isometric minimal immersion of a complete Kahler manifold, biholomorphic to C-2, into R(6).

Books etc

  • 曲面 ---幾何学基礎講義
    古畑 仁 (Single work)
    数学書房 2013 (ISBN: 9784903342382)
  • 北大高校生講座 数学の並木道
    北大数学科, 中村郁 (Contributor第5章 形をはかる話)
    日本評論社 2004 (ISBN: 4535784116)

Conference Activities & Talks

  • Centroaffine surfaces of cohomogeneity one  [Not invited]
    Atsushi Fujioka, Hitoshi Furuhata
    日本数学会2020年度年会幾何学分科会(開催中止)  2020/03
  • Statistical sectional curvature and warped product statistical manifold  [Not invited]
    Naoto Satoh, Hitoshi Furuhata, Izumi Hasegawa
    日本数学会2020年度年会幾何学分科会(開催中止)  2020/03
  • Statistical submanifolds and warped product spaces  [Invited]
    FURUHATA Hitoshi
    The 18th International Conference, Graduate School of Mathematics, Nagoya University, Information Geometry and Affine Differential Geometry III  2019/03
  • Centroaffine surfaces of cohomogeneity one  [Not invited]
    FURUHATA Hitoshi
    研究集会「幾何学のスペクトル」  2018/12
  • 統計多様体,具体例からの入門  [Not invited]
    古畑 仁
    ミニワークショップ 統計多様体の幾何学とその周辺 (10)  2018/11
  • 統計多様体の定曲率空間  [Invited]
    古畑 仁
    福岡大学微分幾何研究集会(Geometry and Analysis 2018)  2018/11
  • Sasakian statistical manifolds and hypersurfaces  [Invited]
    FURUHATA Hitoshi
    PNU-HU Joint Symposium  2017/12
  • Sasakian statistical manifolds and warped product  [Invited]
    FURUHATA Hitoshi
    Seminar on Differential Geometry  2017/11
  • Sasakian statistical manifolds II  [Invited]
    FURUHATA Hitoshi
    3rd conference on Geometric Science of Information  2017/11
  • 中心写像から見た曲面の中心アファイン幾何学  [Invited]
    古畑 仁
    第64回幾何学シンポジウム  2017/08
  • アファイン空間の曲線論入門  [Invited]
    古畑 仁
    第5回水戸幾何セミナー  2017/07
  • 剱持統計多様体  [Invited]
    古畑 仁
    関大微分幾何研究会  2017/06
  • 佐々木構造をもつ統計多様体  [Invited]
    古畑 仁
    名城研究集会「多様体上の計量と幾何構造」  2017/03
  • もう一度はじめから,本当のアファイン曲線  [Invited]
    古畑 仁
    北海道大学幾何学コロキウム  2016/04
  • 正則統計多様体のCR部分多様体  [Invited]
    古畑 仁
    福岡大学微分幾何学研究集会  2015/10
  • Affine differential geometry and surfaces in the projective space  [Invited]
    FURUHATA Hitoshi
    研究集会「Differential Geoemetry with Dajczer」  2015/10
  • 統計多様体の曲率  [Not invited]
    古畑 仁
    ミニワークショップ 統計多様体の幾何学とその周辺 (7)  2015/09
  • 正則統計多様体とその曲率  [Invited]
    古畑 仁
    RIMS共同研究「統計多様体の諸分野への応用」  2014/11
  • ヘッセ多様体とアファイン球面  [Not invited]
    古畑 仁
    ミニワークショップ 統計多様体の幾何学とその周辺 (5)  2014/01
  • 中心アファイン極小曲面の射影極小性  [Invited]
    古畑 仁
    福岡大学微分幾何学研究集会  2013/11
  • 接続の幾何学における部分多様体論にむけて  [Not invited]
    古畑 仁
    ミニワークショップ 統計多様体の幾何学とその周辺 (4)  2013/03
  • Statistical immersions of spaces of constant Hessian curvature  [Invited]
    FURUHATA Hitoshi
    The 8th HU and SNU Symposium on Mathematics -Recent developments of Geometry and Topology-  2012/12
  • Geometry of statistical submanifolds  [Invited]
    FURUHATA Hitoshi
    PADGE2012  2012/08
  • Submanifold theory for statistical manifolds  [Invited]
    FURUHATA Hitoshi
    Workshop on Differential Geometry  2012/06
  • A realization problem for statistical manifolds  [Not invited]
    FURUHATA Hitoshi
    福岡大学微分幾何学研究集会  2011/11
  • Statistical Immersions  [Invited]
    FURUHATA Hitoshi
    RIKEN Workshop on Information Geometry  2011/08
  • 部分多様体の微分幾何学と統計多様体  [Invited]
    古畑 仁
    第13回DCSセミナー  2011/05
  • 定曲率 Hesse 多様体のモデルについて  [Invited]
    古畑 仁
    研究集会「擬リーマン幾何学の展開III」  2010/12
  • Statistical manifolds --- Hypersurfaces and complex structures  [Not invited]
    古畑 仁
    ミニワークショップ 統計多様体の幾何学とその周辺 (2)  2010/10
  • Statistical submanifolds and spaces of constant Hessian sectional curvature  [Invited]
    FURUHATA Hitoshi
    Differential Geometry and its Applications  2010/08
  • Centroaffine Surfaces with Special Center  [Invited]
    古畑 仁
    松江微分幾何学研究会2009  2009/12
  • 統計多様体の微分幾何学入門  [Invited]
    古畑 仁
    北海道大学特異点論セミナー  2009/11
  • Spaces of non-positive constant Hessian curvature  [Invited]
    古畑 仁
    福岡大学微分幾何学研究集会  2009/11
  • Examples of Statistical Manifolds  [Not invited]
    古畑 仁
    ミニワークショップ 統計多様体の幾何学とその周辺 (1)  2009/09

Research Grants & Projects

  • 諸分野に現れるアファインはめ込みの研究
    Date (from‐to) : 2014/04 -2018/03 
    Author : 古畑 仁
  • 部分多様体にあらわれる統計構造の幾何学
    Date (from‐to) : 2009/04 -2013/03 
    Author : 古畑 仁
  • アファインはめ込みの大域的理論と情報幾何学の基礎的研究
    Date (from‐to) : 2003/04 -2006/03 
    Author : 古畑 仁
  • 極小アファイン曲面の計量微分幾何学的研究
    Date (from‐to) : 2001/04 -2003/03 
    Author : 古畑 仁
  • アファインはめ込みの情報幾何学的研究
    Date (from‐to) : 1999/04 -2002/03 
    Author : 古畑 仁
  • ワイル構造および統計構造とアファインはめ込みの幾何学の研究
    Date (from‐to) : 1999/04 -2001/03 
    Author : 古畑 仁
  • Affine Immersions and Statistical Structures
    Date (from‐to) : 2000
  • 一般余次元のアファインはめ込みの分類および構成
    Date (from‐to) : 1997/04 -1999/03 
    Author : 古畑 仁
  • ケーラー多様体からユークリッド空間への等長はめ込みの研究
    Date (from‐to) : 1995/04 -1996/03 
    Author : 古畑 仁

Educational Activities

Teaching Experience

  • Introduction to statistics
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : (条件つき)確率,独立性,確率変数,平均,(共)分散,大数の法則,中心極限定理,推定,検定
  • Basic Geometry
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 曲線と曲面の幾何学
  • Studies on Basic Geometry
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 曲線と曲面の幾何学
  • Calculus II
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 全学教育
    キーワード : 原始関数,積分,重積分,リ-マン和,変数変換
  • Special Lecture on Mathematics
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : ラプラシアン、スペクトル、固有値、固有関数、熱方程式の基本解、閉測地線、臨界点、負曲率多様体、スペクトル剛性

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