[English / Japanese]

Takashi SAKAI's webpage

Research Interests

Integral geometry in Riemannian homogeneous spaces

Hamiltonian stabilities of Lagrangian submanifolds

Publications

Papers:

1. (with O. Ikawa and H. Tasaki) Orbits of Hermann actions, Osaka J. Math. 38 (2001), 923-930.
2. (with H.J. Kang, M. Takahashi and H. Tasaki) Poincare formulas of complex submanifolds, Proc. Japan Acad. 80 (2004), Ser.A, No.6, 110-112.
3. Poincare formula in irreducible Hermitian symmetric spaces, Tokyo J. Math. 26 (2003), No.2, 541-547.
4. (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, 167-170. arXiv:math/0310432
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. 54 (2005), No.5, 1499-1520.
6. Transferred kinematic formulae in two point homogeneous spaces, Tsukuba J. Math. 31 (2007), no. 2, 343-354.
7. (with O. Ikawa and H. Tasaki) Weakly reflective submanifolds and austere submanifolds, J. Math. Soc. Japan. 61, No. 2 (2009), 437-481. arXiv:math/0612384
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. arXiv:0803.2391
9. (wiht H. Iriyeh) Tight Lagrangian surfaces in S^2×S^2, Geom. Dedicata 145, No. 1 (2010), 1-17. arXiv:0809.1536
10. (wiht K. Hashimoto) Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere, Tohoku Math. J. 64, No. 1 (2012), 141-169.
11. (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
12. (with H. Iriyeh and H. Tasaki) Lagrangian intersection theory and Hamiltonian volume minimizing problem, Real and complex submanifolds, Springer Proc. Math. Stat., 106 (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.
19. (with S. Ohno) Area-minimizing cones over minimal embeddings of R-spaces, Josai Mathematical Monographs 13 (2021), 69-91.
20. (with P. Quast) A survey on natural Γ-symmetric structures on R-spaces, In: Differential Geometry and Global Analysis, in Honor of Tadashi Nagano, Contemp. Math. 777 (2022), 185-197.
21. (with R. Akiyama and Y. Sato) Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds, Osaka J. Math. 60 (2023), no. 4, 873-901.

Preprints:

Proceedings:

1. Kinematic formulas in Riemannian homogeneous spaces (Japanese), Surikaisekikenkyusho Kokyuroku 1346 (2003), 113-130.
2. (with H. Iriyeh and H. Ono) Hamiltonian volume minimizing properties of Lagrangian submanifolds, Surikaisekikenkyusho Kokyuroku 1403 (2004), 10-17.
3. Integral geometry and Hamiltonian volume minimizing property, Proceedings of the 9th International Workshop on Differential Geometry, Kyungpook National University, Taegue, Korea, 2004.
4. 3D-XplorMath, Proceedings of the International Workshop "Integrable systems, Geometry and Visualization", Kyushu University, 2004.
5. On the transfer principle in integral geometry, Proceedings of the 10th International Workshop on Differential Geometry, Kyungpook National University, Taegue, Korea, 2005.
6. 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:

1. Integral geometry and Hamiltonian volume minimizing property I, II, The 9th International Workshop on Differential Geomtry, Kyungpook National University, Korea, November 12-13, 2004. [Slide_I] [Slide_II]
2. Transfer principle in integral geometry, 52th Geometry Symposium, [Abstract] [Slide]
3. Transferred kinematic formulae in two point homogeneous spaces, The 10th International Workshop on Differential Geomtry, Kyungpook National University, Korea, November 10-11. 2005. [Slide]
4. Weakly reflective orbits and tangentially degenerate orbits of s-representations, One-Day Workshop on Differential Geometry, National Taiwan University, Taipei, April 1, 2008. [Slide]
5. On a construction of special Lagrangian submanifolds in the complex sphere, Geometry Symposium, Hirosaki University, August 2008. [Abstract] [Slide]
6. Weakly reflective submanifolds and related topics, Mathematical Society of Japan (invited talk), Tokyo Institute of Technology, September 2008. [Abstract] [Slide]
7. Tight Lagrangian surfaces in $S^2 \timesS^2$, Fusion of Integrable Systems and Geometry, Tohoku University, April 2009. [Slide]
8. Absolutely area-minimizing cones over some minimal submanifolds in S^n, Variational problems for curves and surfaces and related topics, Nara Womens University, July 2009. [Slide]
9. Absolutely area-minimizing cones over some minimal submanifolds in the sphere, Submanifold geometry and Lie group actions, Tokyo University of Science, September 2009. [Abstract] [Slide]
10. Global tightness of real forms of flag manifolds, Submanifold geometry-Yuzawa 2009, Echigo-Yuzawa, November 2009. [Abstract]
11. Minimal surfaces with 3D-XplorMath and Maple, GCOE seminar, Kyoto University, December 2009.
12. 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 16-20, 2009. [Slide]
13. Introduction to integral geometry in Riemannian homogeneous spaces, International Mini-Workshop on Integral Geometry and Symmetric spaces, Kyungpook National University, Taegu, Korea, February 22-24, 2010. [Lecture Note] [Slide]
14. Tight Lagrangian submanifolds in some homogeneous Kahler manifolds, The 2nd TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis, National Taiwan University, Taipei, Taiwan, March 21-23, 2010. [Slide]
15. Lagrangian Floer homology and its application to Hamiltonian volume minimizing property, The 4th TIMS-OCAMI Joint International Workshop on Differential Geometry and Geometric Analysis, National Taiwan University, Taipei, Taiwan, March 17-19, 2012. [Slide]
16. 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 1-3, 2012.
17. Minimal submanifolds in Riemannian manifolds, Mini-courses on area-minimizing varieties, Korea Institute for Advanced Study, February 17-18, 2014.
18. Antipodal structure of the intersection of real forms and its applications, Differential Geometry Seminar, California University, Irvine, March 11, 2014.
19. 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 10-12, 2014.
20. S. Ohno and T. Sakai, Area-minimizing cones over minimal embeddings of R-spaces, The 9th OCAMI-KNUHGRG Joint Differential Geometry Workshop on Submanifold Geometry and Lie Theory, Osaka City University, February 12-14, 2015.
21. 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 Hermitian-Grassmannian Submanifolds and Its Applications, National Institute for Mathematical Sciences, Daejeon, Korea, October 26-28, 2015.
22. Biharmonic homogeneous submanifolds in compact symmetric spaces, The 11th OCAMI-RIRCM Joint Differential Geometry Workshop on Submanifolds and Lie Theory, Osaka City University, March 20-23, 2016.
23. 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 26-30, 2016.
24. The intersection of two real flag manifolds in a complex flag manifold, The First Japan-Taiwan Joint Conference on Differential Geometry & the 8th TIMS-OCAMI-WASEDA Joint International Workshop on Differential Geometry and Geometric Analysis, Waseda University, December 13-17, 2016.
25. 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 28-30, 2017.
26. Biharmonic submanifolds in compact symmetric spaces and compact Lie groups, Geometry Seminar, Korea Institute for Advanced Study, Seoul, Korea, September 27, 2017.
27. The intersection of two real flag manifolds in a complex flag manifold, The 15th OCAMI-RIRCM Joint Differential Geometry Workshop & The 3rd OCAMI-KOBE-WASEDA Joint International Workshop on Differential Geometry and Integrable Systems "Geometry of Submanifolds and Integrable Systems", Osaka City University, March 26-30, 2018.
28. S. Ohno, T. Sakai and Y. Terauchi, Antipodal sets of generalized s-manifolds, Special Session: Riemannian Geometry and Related Fields, 2018 Joint Meeting of the Korean Mathematical Society and the German Mathematical Society, COEX, Seoul, Korea, October 3-6, 2018.
29. S. Ohno, T. Sakai and Y. Terauchi, Antipodal sets of generalized s-manifolds, AMS Sectional Meeting, University of Hawaii at Manoa, March 22-24, 2019.
30. Toward classification of biharmonic homogeneous hypersurfaces in compact symmetric spaces, Workshop on the Isoparametric Theory, Beijin Nomal University, Beijin, China, June 2-6, 2019.
31. Variational problems for integral invariants of the second fundamental form of a map between Riemannian manifolds, The 2nd Shot of The 13th MSJ-SI "Differential Geometry and Integrable Systems" The 5th International Workshop Geometry of Submanifolds and Integrable Systems, Takamatsu Symbol Tower, November 26-December 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)

3D-XplorMath

Last update : April 2, 2024