[English / Japanese]
Takashi SAKAI's webpage
Takashi SAKAI

Professor

Department of Mathematical Sciences
Tokyo Metropolitan University
11 MinamiOsawa, Hachiojishi,
Tokyo 1920397, JAPAN

Office 
: 
8631 
Tel 
: 
0426772458 
Fax 
: 
0426772481 
Email 
: 
sakait (at) tmu.ac.jp 
Office Hour 
: 
Tuesday 13:0014:30 

Visiting Professor
Osaka Central Advanced Mathematical Institute (OCAMI)

Research Interests
Integral geometry in Riemannian homogeneous spaces
Hamiltonian stabilities of Lagrangian submanifolds
Publications
Papers:

(with O. Ikawa and H. Tasaki) Orbits of Hermann actions,
Osaka J. Math. 38 (2001), 923930.

(with H.J. Kang, M. Takahashi and H. Tasaki) Poincare formulas of complex submanifolds,
Proc. Japan Acad. 80 (2004), Ser.A, No.6, 110112.

Poincare formula in irreducible Hermitian symmetric spaces,
Tokyo J. Math. 26 (2003), No.2, 541547.

(with H. Iriyeh and H. Ono)
Integral geometry and Hamiltonian volume minimizing property
of a totally geodesic Lagrangian torus in S^2 x S^2,
Proc. Japan Acad. 79 (2003), Ser.A, No.10, 167170.
arXiv:math/0310432

(with H.J. Kang and Y.J. Suh)
Kinematic formulas for integral invariants of degree two in real space forms,
Indiana Univ. Math. J. 54 (2005), No.5, 14991520.

Transferred kinematic formulae in two point homogeneous spaces,
Tsukuba J. Math. 31 (2007), no. 2, 343354.

(with O. Ikawa and H. Tasaki) Weakly reflective submanifolds and austere submanifolds,
J. Math. Soc. Japan. 61, No. 2 (2009), 437481.
arXiv:math/0612384

(with O. Ikawa and H. Tasaki)
Liealgebraic characterization of tangentially degenerate orbits of srepresentations,
Differential Geom. Appl. 28, No. 1 (2010), 81101.
arXiv:0803.2391

(wiht H. Iriyeh)
Tight Lagrangian surfaces in S^2~S^2,
Geom. Dedicata 145, No. 1 (2010), 117.
arXiv:0809.1536

(wiht K. Hashimoto)
Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere,
Tohoku Math. J. 64, No. 1 (2012), 141169.

(wiht H. Iriyeh and H. Tasaki)
Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type,
to appear in J. Math. Soc. Japan.
arXiv:1108.0260

(with H. Iriyeh and H. Tasaki)
Lagrangian intersection theory and Hamiltonian volume minimizing problem,
Real and complex submanifolds, Springer Proc. Math. Stat., 106 (2014), 391399.

(with S. Ohno and H. Urakawa)
Biharmonic homogeneous hypersurfaces in compact symmetric spaces,
Differential Geom. Appl. 43 (2015), 155179.

(with S. Ohno and H. Urakawa)
Biharmonic homogeneous submanifolds in compact symmetric spaces,
HermitianGrassmannian submanifolds, Springer Proc. Math. Stat., 203 (2017), 323333.

(with S. Ohno and H. Urakawa)
Rigidity of transversally biharmonic maps between foliated Riemannian manifolds,
Hokkaido Math. J. 47 (2018), no. 3, 637654.

(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), 8798.

(with S. Ohno and H. Urakawa)
Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups,
Hiroshima Math. J. 49 (2019), no. 1, 47115.

(with P. Quast)
Natural symmetric structures on Rspaces,
J. Math. Pures Appl. (9) 141 (2020), 371383.

(with S. Ohno)
Areaminimizing cones over minimal embeddings of Rspaces,
Josai Mathematical Monographs 13 (2021), 6991.

(with P. Quast)
A survey on natural symmetric structures on Rspaces,
In: Differential Geometry and Global Analysis, in Honor of Tadashi Nagano,
Contemp. Math. 777 (2022), 185197.

(with R. Akiyama and Y. Sato)
Variational problems for integral invariants of the second fundamental form of a map between pseudoRiemannian manifolds,
Osaka J. Math. 60 (2023), no. 4, 873901.
Preprints:
Proceedings:

Kinematic formulas in Riemannian homogeneous spaces (Japanese),
Surikaisekikenkyusho Kokyuroku 1346 (2003), 113130.

(with H. Iriyeh and H. Ono)
Hamiltonian volume minimizing properties of Lagrangian submanifolds,
Surikaisekikenkyusho Kokyuroku 1403 (2004), 1017.

Integral geometry and Hamiltonian volume minimizing property,
Proceedings of the 9th International Workshop on Differential Geometry,
Kyungpook National University, Taegue, Korea, 2004.

3DXplorMath,
Proceedings of the International Workshop
"Integrable systems, Geometry and Visualization",
Kyushu University, 2004.

On the transfer principle in integral geometry,
Proceedings of the 10th International Workshop on Differential Geometry,
Kyungpook National University, Taegue, Korea, 2005.

Introduction to integral geometry in Riemannian homogeneous spaces,
Proceedings of the 14th International Workshop on Differential Geometry and Related Fields,
Kyungpook National University, Taegue, Korea, 2010.
Talks:

Integral geometry and Hamiltonian volume minimizing property I, II,
The 9th International Workshop on Differential Geomtry,
Kyungpook National University, Korea, November 1213, 2004.
[Slide_I]
[Slide_II]

Transfer principle in integral geometry, 52th Geometry Symposium,
[Abstract]
[Slide]

Transferred kinematic formulae in two point homogeneous spaces,
The 10th International Workshop on Differential Geomtry,
Kyungpook National University, Korea, November 1011. 2005.
[Slide]

Weakly reflective orbits and tangentially degenerate orbits of srepresentations,
OneDay Workshop on Differential Geometry,
National Taiwan University, Taipei, April 1, 2008.
[Slide]

On a construction of special Lagrangian submanifolds in the complex sphere,
Geometry Symposium, Hirosaki University, August 2008.
[Abstract]
[Slide]

Weakly reflective submanifolds and related topics,
Mathematical Society of Japan (invited talk), Tokyo Institute of Technology, September 2008.
[Abstract]
[Slide]

Tight Lagrangian surfaces in $S^2 \timesS^2$,
Fusion of Integrable Systems and Geometry, Tohoku University, April 2009.
[Slide]

Absolutely areaminimizing cones over some minimal submanifolds in S^n,
Variational problems for curves and surfaces and related topics,
Nara Womens University, July 2009.
[Slide]

Absolutely areaminimizing cones over some minimal submanifolds in the sphere,
Submanifold geometry and Lie group actions,
Tokyo University of Science, September 2009.
[Abstract]
[Slide]

Global tightness of real forms of flag manifolds,
Submanifold geometryYuzawa 2009, EchigoYuzawa, November 2009.
[Abstract]

Minimal surfaces with 3DXplorMath and Maple,
GCOE seminar, Kyoto University, December 2009.

Explicit expressions of kinematic formulae in Riemannian homogeneous spaces,
2009 Joint Meeting of the Korean Mathematical Society and the American Mathematical Society,
Ewha Womans University, Seoul, Korea, December 1620, 2009.
[Slide]

Introduction to integral geometry in Riemannian homogeneous spaces,
International MiniWorkshop on Integral Geometry and Symmetric spaces,
Kyungpook National University, Taegu, Korea, February 2224, 2010.
[Lecture Note]
[Slide]

Tight Lagrangian submanifolds in some homogeneous Kahler manifolds,
The 2nd TIMSOCAMI Joint International Workshop on
Differential Geometry and Geometric Analysis,
National Taiwan University, Taipei, Taiwan, March 2123, 2010.
[Slide]

Lagrangian Floer homology and its application to Hamiltonian volume minimizing property,
The 4th TIMSOCAMI Joint International Workshop on
Differential Geometry and Geometric Analysis,
National Taiwan University, Taipei, Taiwan, March 1719, 2012.
[Slide]

Antipodal structure of the intersection of real forms in a complex flag manifold,
The 16th International Workshop on Differential Geometry,
Kyungpook National University, Taegu, Korea, November 13, 2012.

Minimal submanifolds in Riemannian manifolds,
Minicourses on areaminimizing varieties,
Korea Institute for Advanced Study, February 1718, 2014.

Antipodal structure of the intersection of real forms and its applications,
Differential Geometry Seminar,
California University, Irvine, March 11, 2014.

H. Iriyeh, T. Sakai and H. Tasaki,
Lagrangian intersection theory and Hamiltonian volume minimizing problem,
ICM Satellite Conference on "Real and Complex Submanifolds",
National Institute for Mathematical Sciences, Daejeon, Korea, August 1012, 2014.

S. Ohno and T. Sakai,
Areaminimizing cones over minimal embeddings of Rspaces,
The 9th OCAMIKNUHGRG Joint Differential Geometry Workshop on Submanifold Geometry and Lie Theory,
Osaka City University, February 1214, 2015.

O. Ikawa, H. Iriyeh, T. Okuda, T. Sakai and H. Tasaki,
Antipodal structure of the intersection of real flag manifolds in a complex flag manifold II,
The 19th International Workshop on HermitianGrassmannian Submanifolds and Its Applications,
National Institute for Mathematical Sciences, Daejeon, Korea, October 2628, 2015.

Biharmonic homogeneous submanifolds in compact symmetric spaces,
The 11th OCAMIRIRCM Joint Differential Geometry Workshop on Submanifolds and Lie Theory,
Osaka City University, March 2023, 2016.

S. Ohno, T. Sakai and H. Urakawa,
Biharmonic homogeneous submanifolds in compact symmetric spaces,
The 20th International Workshop on Hermitian Symmetric Spaces and Submanifolds,
Kyungpook National University, Daegu, Korea, July 2630, 2016.

The intersection of two real flag manifolds in a complex flag manifold,
The First JapanTaiwan Joint Conference on Differential Geometry & the 8th TIMSOCAMIWASEDA Joint International Workshop on Differential Geometry and Geometric Analysis,
Waseda University, December 1317, 2016.

The intersection of two real flag manifolds in a complex flag manifold,
Special Session: On Hermitian Symmetric Spaces and Twisted Manifolds,
2017 Korean Mathematical Society Spring Meeting,
Chosun University, Gwangju, Korea, April 2830, 2017.

Biharmonic submanifolds in compact symmetric spaces and compact Lie groups,
Geometry Seminar, Korea Institute for Advanced Study, Seoul, Korea, September 27, 2017.

The intersection of two real flag manifolds in a complex flag manifold,
The 15th OCAMIRIRCM Joint Differential Geometry Workshop & The 3rd OCAMIKOBEWASEDA Joint International Workshop on Differential Geometry and Integrable Systems "Geometry of Submanifolds and Integrable Systems",
Osaka City University, March 2630, 2018.

S. Ohno, T. Sakai and Y. Terauchi,
Antipodal sets of generalized smanifolds,
Special Session: Riemannian Geometry and Related Fields,
2018 Joint Meeting of the Korean Mathematical Society and the German Mathematical Society,
COEX, Seoul, Korea, October 36, 2018.

S. Ohno, T. Sakai and Y. Terauchi,
Antipodal sets of generalized smanifolds,
AMS Sectional Meeting, University of Hawaii at Manoa, March 2224, 2019.

Toward classification of biharmonic homogeneous hypersurfaces in compact symmetric spaces,
Workshop on the Isoparametric Theory, Beijin Nomal University,
Beijin, China, June 26, 2019.

Variational problems for integral invariants of the second fundamental form of a map between Riemannian manifolds,
The 2nd Shot of The 13th MSJSI "Differential Geometry and Integrable Systems"
The 5th International Workshop Geometry of Submanifolds and Integrable Systems,
Takamatsu Symbol Tower, November 26December 1, 2022.
Links
Department of Mathematical Sciences,
Graduate School of Science,
Tokyo Metropolitan University
Mathematical Society of Japan
Geometry section of the MSJ
OCAMI (Osaka City University Advanced Mathematical University)
3DXplorMath
Last update : April 2, 2024