List of Publications


Published books: 

1. Vector Analysis and Differential Geometry enlightened by Integral Formulas,
Kyoritsu Shuppan CO., Ltd., ISBN:978-4-320-11475-3, (2022).view

2. Submanifold Geometry Hidden in Theoretical Physics, Kyoritsu Shuppan CO., Ltd.,
ISBN:978-4-320-11440-1, (2021).view

3. Mean Curvature Flow-Time Evolution of Submanifolds, Kyoritsu Shuppan CO., Ltd.,
ISBN:978-4-320-11376-3, (2019).view

Published papers: 

1. Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space
and its application to gauge theory, Calc. Var. Partial Differential Equations
(to appear).

2. Translators invariant under hyperpolar actions, Kodai Math. J. (to appear)
(with Tomoki Fujii).

3. Isoparametric submanifolds in Hilbert spaces and holonomy maps,
Illinois Journal of Mathematics, vol. 67 (2023) 153-170. view

4. The preservability of the curvature-adaptedness along the mean curvature flow, Differential Geometry and its Applications vol. 84 (2022) 101931 (15 pages). view

5. The behaviour of the mean curvature flow for pinched submanifolds in rank one symmetric spaces, Osaka Journal of Mathematics, vol. 59 (2022) 905-950. view

6. Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space, Math. Nachrichten vol. 293 (2020) 923-944 (with Honoka Kobayashi). view

7. Isoparametric submanifolds admitting a reflective focal submanifold in symmetric spaces of non-compact type, Osaka J. Math. vol. 57 (2020) 207-246. view

8. Calabi-Yau structures and special Lagrangian submanifolds of complexified symmetric spaces, Illinois J. Math. vol. 63 (2019) 575-600. view

9. Equifocal submanifolds in a symmetric space and the infinite dimensional geometry, SUGAKU EXPOSITIONS, vol. 32 (2019) 25-56. view

10. Mean curvature flow of certain kind of isoparametric foliations on non-cpmpact symmetric spaces, CUBO A Mathematical Journal vol. 20 (2018) 13-30. view

11. A modified mean curvature flow in Euclidean space and soap bubbles in symmetric spaces, Geometriae Dedicata vol. 195 (2018) 1-17. view

12. Gauss maps of the Ricci-mean curvature flow, Geometriae Dedicata vol. 194 (2018) 169-185. (with Hikaru Yamamoto). view

13. The mean curvature flow for invariant hypersurfaces in a Hilbert space with an almost free group action, Asian J. Math. vol. 21 (2017) 953-980. view

14. Homogeneity of infinite dimensional anti-Kaehler isoparametric submanifolds II, Tokyo J. Math. vol. 40 (2017) 301-337. view

15. Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type, Calc. Var. Partial Differential Equations vol. 56, (2017) (51pages). view

16. A holonomy invariant anisotropic surface energy in a Riemannian manifold, Differential Geom. Appl. vol. 44 (2016) 98-121. view

17. The inverse mean curvature flow in rank one symmetric spaces of non-compact type, Kyushu J. Math. vol.69 (2015) 259-284 (with Yusuke Sakai). view

18. On the indices of minimal orbits of Hermann actions, Hokkaido Math. J. vol.44 (2015) 251-275. view

19. 対称空間内の等焦部分多様体と無限次元幾何, 数学・論説 67 日本数学会 (2015) 26-54. view

20. The Regularized Mean Curvature Flow for Invariant Hypersurfaces in a Hilbert Space, Seoul ICM 2014, Satellite Conference on Real and Complex Submanifolds, Springer Proceedings in Mathematics & Statistics vol. 106 (2015) pp 437-452. view

21. Research of submanifolds in symmetric spaces by using the complexification and the infinite dimensional geometry, SUT J. Math. (Fiftieth Anniversary Issue) vol. 50 (2014) 103-129. view

22. The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry, SUT J. Math. (Fiftieth Anniversary Issue) vol. 50 (2014) 271-295. view

23. A Cartan type identity for isoparametric hypersurfaces in symmetric spaces, Tohoku Math. J. vol. 66 (2014) 435-454. view

24. The constancy of principal curvatures of curvature-adapted submanifolds in symmetric spaces, Differential Geom. Appl. vol. 35 (2014) 103-113. view

25. Homogeneity of infinite dimensional anti-Kaehler isoparametric submanifolds, Tokyo J. Math. vol. 37 (2014) 159-178. view

26. Collapse of the mean curvature flow for isoparametric submanifolds in non-cmpact symmetric spaces, Kodai Math. J. vol. 37 (2014) 355-382. view

27. Examples of certain kind of minimal orbits of Hermann actions, Hokkaido Math. J. vol. 43 (2014) 21-42. view

28. Collapse of the mean curvature flow for equifocal submanifolds, Asian J. Math. vol. 15 (2011) 101-128. view

29. Hermann type actions on a pseudo-Riemannian symmetric space, Tsukuba J. Math. vol. 34 (2010) 137-172. view

30. On curvature-adapted and proper complex equifocal submanifolds, Kyungpook Math. J. vol. 50 (2010) 509-536. view

31. Examples of a complex hyperpolar action without singular orbit, Cubo A Math. J. vol. 12 (2010) 131-147. view

32. The homogeneous slice theorem for the complete complexification of a proper complex equifocal submanifold, Tokyo J. of Math. vol. 33 (2010) 1-30. view

33. On non-existenceness of equifocal submanifolds with non-flat section, Asian J. of Math. vol. 12 (2008) 421-442. view

34. A Chevalley type restriction theorem for a proper complex equifocal submanifold, Kodai Math. J. vol. 30 (2007) 280-296. view

35. Complex hyperpolar actions with a totally geodesic orbit, Osaka J. Math. vol. 44 (2007) 491-503. view

36. A splitting theorem for proper compex equifocal submanifolds, Tohoku Math. J. vol. 58 (2006) 393-417. view

37. The variational formulas for the volume function in the equiaffine geometry, Hokkaido Math. J. vol. 35 (2006) 719-751. view

38. Complex equifocal submanifolds and infinite dimensional anti-Kaehlerian isoparametric submanifolds, Tokyo J. Math. vol. 28 (2005) 201-247. view

39. Actions of Hermann type and proper complex equifocal submani- folds, Osaka J. Math. vol. 42 (2005) 599-611. view

40. Blaschke Dupin hypersurfaces and equiaffine tubes, Results Math. vol. 48 (2005) 97-108. view

41. The quadratic slice theorem and the equiaffine tube theorem for equiaffine Dupin
hypersurfaces, Results Math. vol. 47 (2005) 69-92. view

42. The Gauss-Bonnet and Chern-Lashof theorems in a simply connected symmetric space of compact type, Tokyo J. Math. vol. 28 (2005) 483-497. view

43. Submanifold geometries in a symmetric space of non-compact type and a pseudo-Hilbert space, Kyushu J. Math, vol. 58 (2004) 167-202. view

44. A generalization of Lelieuvre's formula for equiaffine immersions of general codimension, Results Math. vol. 43 (2003) 150-155. view

45. Theorems of Gauss-Bonnet and Chern-Lashof types in a simply connected symmetric space of non-positive curvature, Tokyo J. Math. vol. 26 (2003) 527-539. view

46. On focal points of submanifolds in symmetric spaces, SUT J. Math. vol. 39 (2003) 171-181. view

47. On proper Fredholm submanifolds in a Hilbert space arising from submanifolds in a symmetric space, Japan J. Math. vol. 28 (2002) 61-80. view

48. The total absolute curvature of an equiaffine immersion, Results Math. vol. 42 (2002) 81-106. view

49. Tubes of non-constant radius in symmetric spaces, Kyushu J. Math. vol. 56 (2002) 267-291. view

50. Equiaffine immersions of general codimension and its transversal volume element map, Results Math. vol. 39 (2001) 276-291 (with Kouji Takekuma). view

51. An extrinsic decomposition theorem and a slant tube theorem for a curvature netted hypersurface, Results Math. vol. 39 (2001) 245-273. view

52. The Lipschitz-Killing curvature for an equiaffine immersion and theorems of Gauus-Bonnet type and Chern-Lashof type, Results Math. vol. 39 (2001) 230-244. view

53. Ehresmann connections for a foliated manifold and certain kinds of rectangles without terminal vertx, Kodai Math. J. vol. 22 (1999) 402-423. view

54. Generalized helical immersions of a Riemannian manifold all of whose geodesics are closed into a Euclidean space, Tsukuba J. Math. vol. 22 (1998) 811-824. view

55. A theorem of Pick-Berwald type for a totally umbilical affine immersion of general codimension, SUT J. Math. vol. 34 (1998) .169-177. (with Yoko Torisawa) view

56. Generalized helical immersions, Tsukuba J. Math. vol. 22 (1998) 407-425. view

57. On proper helices and extrinsic spheres in pseudo-Riemannian geometry, Tsukuba J. Math. vol. 20 (1996) 263-280. view

58. The decomposition of curvature netted hypersurfaces, Geometriae Dedicata vol. 54 (1995) 1-11. view

59. Ehresmann connections for a foliation on a manifold with boundry, SUT J. Math. vol. 30 (1994) 147-158. view

60. On tubes of nonconstant radius, Tsukuba J. Math. vol. 17 (1993) 267-286. view

61. Totally umbilic orthogonal nets and decomposition theorems, Saitam Math. J. vol. 10 (1992) 1-20. view

62. Foliations on a Riemannian manifold and Ehresmann connections, Indiana Univ. Math. J. vol. 40 (1991) 277-292. view

63. Totally umbilic foliations and decomposition theorems, Saitama Math. J. vol. 8 (1990) 1-18. view

64. Proper isoparametric semi-Riemannian submanifolds in a semi-Riemannian space form, Tsukuba J. Math. vol. 13 (1989) 131-146. view

65. Congruence theorem for proper semi-Riemannian hyperdurfaces in a real space form, Yokohama Math. J. vol. 35 (1987) 123-136. view

Click here (MathSciNet)or here about list of all publications.

Click here (arXiv)list of unpublished papers.
  
  arXiv:1310.0649v4  (Version up date:15 January, 2014)
  arXiv:1309.4225v5  (Version up date : 14 January.2014)
  arXiv:1010.1652v4  (Version up date:30 Sptember, 2013)
  arXiv:1210.2539v2  (Version up date : 12 September, 2013)
  arXiv:1001.3514v5  (Version up date : 25 February, 2013)
  arXiv:1212.3911v2  (Version up date : 26 February, 2013)
  arXiv:1209.1933v1  (Up date:11 September 2012)
  arXiv:0807.1606v3  (Version Up date:28 Decmber, 2010)
  arXiv:0902.1375v3  (Version Up date:13 December, 2010)
  arXiv:0908.3086v5  (Version Up date:23 April, 2010)
  arXiv:1001.3508v3  (Version up date:23 April, 2010)
  arXiv:0807.1601v3  (Version up date:23 April, 2010)
  arXiv:0807.1607v3  (Version up date:15 March, 2010)
  arXiv:0807.1579v3  (Version up date:14 February, 2010)


List of Invited Lectures

1. The regularized mean curvature flow for invariant hypersurfaces in a Hilbert space
The name of conference:Seoul ICM 2014 (International Congress of Mathematicians)
-Satellite Conference on Real and Complex Submanifolds 
Place : National Institute for Mathematical Science、Korea 
Date:10-12 October, 2014
2. Title:The regularized mean curvature flow for invariant hypersurfaces in a Hilbert space
with an almost free Lie group action
The name of conference:Development of group actions and submanifold theory,
Place:Research of Institute of Mathematical Science in Kyoto University, Japan
Date:26 June, 2014
3. Title:The mean curvature flow for a convex hypersurface
The name of conference:Mini International Workshop on Quaternionic hyperbolic space,
Osserman $4$-manifolds and mean curvature flow
Place:Kyungpook National University, Korea
Date:18 December, 2013
4. Title:The mean curvature flow for a mean convex hypersurface
The name of conference:Mini International Workshop on Quaternionic hyperbolic space,
Osserman $4$-manifolds and mean curvature flow
Place:Kyungpook National University, Korea
Date:18 December, 2013
5. Title:The mean curvature flow for an equifocal submanifold
The name of conference:Mini International Workshop on Quaternionic hyperbolic space, Osserman $4$-manifolds and mean curvature flow
Place:Kyungpook National University, Korea
Date:19 December, 2013
6. Title:The mean curvature flow for a complex equifocal submanifold
The name of conference:Mini International Workshop on Quaternionic hyperbolic space,
Osserman $4$-manifolds and mean curvature flow
Place:Kyungpook National University, Korea
Date:19 December, 2013
7. Title:The regularized mean curvature flow for an invariant hypersurface in a Hilbert space
The name of conference:Mini International Workshop on Quaternionic hyperbolic space,
Osserman $4$-manifolds and mean curvature flow
Place:Kyungpook National University, Korea
Date:20 December, 2013
8. Title : Certain kind of isoparametric submanifolds in symmetric spaces of non-compact type and Hermann actions
The name of conference : The 6th OCAMI-KNUGRG Joint Differential Geometry Workshop on Submnaifold Theory in Symmetric spaces and Lie Theory in Finite and Infinite Dimensions
Place:Osaka City University
Date:2 February, 2013 (The PDF file used in this talk)
9. Title: The mean curvature flow for an isoparametric submanifold in a symmetric space
The name of conference:広島幾何学研究集会2012
Date :4 October, 2012 (The PDF file used in this talk)
10. Title:The classification of a certain kind of isoparametric submanifold in a symmetric space of non-compact type
The name of conference:Submanifold Geometry and Lie group action 2012
Place:Tokyo University of Science
Date : 4 September, 2012 (The PDF file used in this talk)
11. Title:The classification of a certain kind of isoparametric submanifold in a symmetric space of non-compact type
The name of conference:部分多様体の微分幾何学及び関連課題 ~前田定廣先生還暦記念研究集会~
Place :Saga University
Date :5 August, 2012 (The PDF file used in this talk)

Plan of talks