SAKAI Takashi
教授
酒井 高司 サカイ タカシ さかい たかし
プロフィール
最終学歴・学位
博士（理学）
専門・研究分野
微分幾何学・部分多様体論
研究
研究テーマ
リー理論的手法をもとにリーマン対称空間内の部分多様体に関する幾何学的変分問題について研究を行っている。特に、大域的な対称性や体積最小性など顕著な性質を持つ部分多様体に興味を持っている。また、ケーラー多様体内のラグランジュ部分多様体の幾何学的性質についても研究を行っている。
研究キーワード
微分幾何学，部分多様体，幾何学的変分問題，対称空間，等質空間
研究イメージ
研究紹介
詳細情報
[1] (with O. Ikawa and H. Tasaki) Orbits of Hermann actions, Osaka J. Math. Vol.38, (2001), 923-930.
[2] Poincare formula in irreducible Hermitian symmetric spaces, Tokyo J. Math. Vol.26 No.2, (2003), 541-547.
[3] (with H. Iriyeh and H. Ono) Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S^2×S^2, Proc. Japan Acad. Vol.79, Ser.A, No.10, (2003), 167-170.
[4] (with H. J. Kang, M. Takahashi and H. Tasaki) Poincare formulas of complex submanifolds, Proc. Japan Acad. Vol.80, Ser.A, No.6, (2004), 110-112.
[5] (with H. J. Kang and Y. J. Suh) Kinematic formulas for integral invariants of degree two in real space forms, Indiana Univ. Math. J. Vol.54, No.5 (2005), 1499-1520.
[6] Transferred kinematic formulae in two point homogeneous spaces,
Tsukuba J. Math. Vol.31, No.2, (2007), 343-354.
[7] (with O. Ikawa and H. Tasaki) Weakly reflective submanifolds and austere submanifolds, J. Math. Soc. Japan. Vol.61, No.2 (2009), 437-481.
[8] (with O. Ikawa and H. Tasaki) Lie-algebraic characterization of tangentially degenerate orbits of s-representations, Differential Geom. Appl. 28, No. 1 (2010), 81-101.
[9] (with H. Iriyeh) Tight Lagrangian surfaces in S^2×S^2, Geom. Dedicata 145, No. 1 (2010), 1-17.
[10] (with K. Hashimoto) Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere, Tohoku Math. J. 64, No. 1 (2012), 141-169.
[11] (with H. Iriyeh and H. Tasaki) Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type, J. Math. Soc. Japan 65, No. 4, (2013), 1135-1151.
[12] (with H. Iriyeh and H. Tasaki) Lagrangian intersection theory and Hamiltonian volume minimizing problem, Springer Proceedings in Mathematics and Statistics, ICM Satellite Conference on "Real and Complex Submanifolds", Daejeon, Korea, (2014), 391-399.
[13] (with S. Ohno and H. Urakawa) Biharmonic homogeneous hypersurfaces in compact symmetric spaces, Differential Geom. Appl. 43 (2015), 155-179.
[14] (with S. Ohno and H. Urakawa) Biharmonic homogeneous submanifolds in compact symmetric spaces, Hermitian-Grassmannian submanifolds, Springer Proc. Math. Stat., 203 (2017), 323-333.
[15] (with S. Ohno and H. Urakawa) Rigidity of transversally biharmonic maps between foliated Riemannian manifolds, Hokkaido Math. J. 47 (2018), no. 3, 637-654.
[16] (with H. Iriyeh and H. Tasaki) On the structure of the intersection of real flag manifolds in a complex flag manifold, Adv. Stud. Pure Math. 82 (2019), 87-98.
[17] (with S. Ohno and H. Urakawa) Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups,
Hiroshima Math. J. 49 (2019), no. 1, 47-115.
[18] (with P. Quast) Natural Γ-symmetric structures on R-spaces, J. Math. Pures Appl. (9) 141 (2020), 371-383.
[2] Poincare formula in irreducible Hermitian symmetric spaces, Tokyo J. Math. Vol.26 No.2, (2003), 541-547.
[3] (with H. Iriyeh and H. Ono) Integral geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S^2×S^2, Proc. Japan Acad. Vol.79, Ser.A, No.10, (2003), 167-170.
[4] (with H. J. Kang, M. Takahashi and H. Tasaki) Poincare formulas of complex submanifolds, Proc. Japan Acad. Vol.80, Ser.A, No.6, (2004), 110-112.
[5] (with H. J. Kang and Y. J. Suh) Kinematic formulas for integral invariants of degree two in real space forms, Indiana Univ. Math. J. Vol.54, No.5 (2005), 1499-1520.
[6] Transferred kinematic formulae in two point homogeneous spaces,
Tsukuba J. Math. Vol.31, No.2, (2007), 343-354.
[7] (with O. Ikawa and H. Tasaki) Weakly reflective submanifolds and austere submanifolds, J. Math. Soc. Japan. Vol.61, No.2 (2009), 437-481.
[8] (with O. Ikawa and H. Tasaki) Lie-algebraic characterization of tangentially degenerate orbits of s-representations, Differential Geom. Appl. 28, No. 1 (2010), 81-101.
[9] (with H. Iriyeh) Tight Lagrangian surfaces in S^2×S^2, Geom. Dedicata 145, No. 1 (2010), 1-17.
[10] (with K. Hashimoto) Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere, Tohoku Math. J. 64, No. 1 (2012), 141-169.
[11] (with H. Iriyeh and H. Tasaki) Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type, J. Math. Soc. Japan 65, No. 4, (2013), 1135-1151.
[12] (with H. Iriyeh and H. Tasaki) Lagrangian intersection theory and Hamiltonian volume minimizing problem, Springer Proceedings in Mathematics and Statistics, ICM Satellite Conference on "Real and Complex Submanifolds", Daejeon, Korea, (2014), 391-399.
[13] (with S. Ohno and H. Urakawa) Biharmonic homogeneous hypersurfaces in compact symmetric spaces, Differential Geom. Appl. 43 (2015), 155-179.
[14] (with S. Ohno and H. Urakawa) Biharmonic homogeneous submanifolds in compact symmetric spaces, Hermitian-Grassmannian submanifolds, Springer Proc. Math. Stat., 203 (2017), 323-333.
[15] (with S. Ohno and H. Urakawa) Rigidity of transversally biharmonic maps between foliated Riemannian manifolds, Hokkaido Math. J. 47 (2018), no. 3, 637-654.
[16] (with H. Iriyeh and H. Tasaki) On the structure of the intersection of real flag manifolds in a complex flag manifold, Adv. Stud. Pure Math. 82 (2019), 87-98.
[17] (with S. Ohno and H. Urakawa) Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups,
Hiroshima Math. J. 49 (2019), no. 1, 47-115.
[18] (with P. Quast) Natural Γ-symmetric structures on R-spaces, J. Math. Pures Appl. (9) 141 (2020), 371-383.
OCAMI Association Special Prize (2008)
日本数学会会員
- 線形代数I e
- 幾何学特別講義III
- 幾何学概論（3）
- 数理科学演習
- 数理科学特別演習
- 幾何学特別講義1
- 先端幾何学特別講義1
- 数学の歴史
- 組織再編前旧課程の同時開講科目等が含まれており、掲載されている全ての科目を開講するわけではありません。
関連HOT TOPICS
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研究室
8号館631号室
オフィスアワー
火曜3時限 13:00～14:30
内線番号
内線3138
メールアドレス
sakai-t●tmu.ac.jp
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