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. Isoparametric submanifolds in Hilbert spaces and holonomy maps,
Illinois Journal of Mathematics, vol. 67 (2023) 153-170. view
3. The preservability of the curvature-adaptedness along the mean curvature
flow, Differential Geometry and its Applications vol. 84 (2022) 101931
(15 pages). view
4. 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
5. Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter
space, Math. Nachrichten vol. 293 (2020) 923-944 (with Honoka Kobayashi).
view
6. Isoparametric submanifolds admitting a reflective focal submanifold
in symmetric spaces of non-compact type, Osaka J. Math. vol. 57 (2020)
207-246. view
7. Calabi-Yau structures and special Lagrangian submanifolds of complexified
symmetric spaces, Illinois J. Math. vol. 63 (2019) 575-600. view
8. Equifocal submanifolds in a symmetric space and the infinite dimensional
geometry, SUGAKU EXPOSITIONS, vol. 32 (2019) 25-56. view
9. Mean curvature flow of certain kind of isoparametric foliations on non-cpmpact
symmetric spaces, CUBO A Mathematical Journal vol. 20 (2018) 13-30. view
10. A modified mean curvature flow in Euclidean space and soap bubbles
in symmetric spaces, Geometriae Dedicata vol. 195 (2018) 1-17. view
11. Gauss maps of the Ricci-mean curvature flow, Geometriae Dedicata vol.
194 (2018) 169-185. (with Hikaru Yamamoto). view
12. 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
13. Homogeneity of infinite dimensional anti-Kaehler isoparametric submanifolds
II, Tokyo J. Math. vol. 40 (2017) 301-337. view
14. 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
15. A holonomy invariant anisotropic surface energy in a Riemannian manifold,
Differential Geom. Appl. vol. 44 (2016) 98-121. view
16. 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
17. On the indices of minimal orbits of Hermann actions, Hokkaido Math.
J. vol.44 (2015) 251-275. view
18. 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
19. 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
20. 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
21. The complexifications of pseudo-Riemannian manifolds and anti-Kaehler
geometry, SUT J. Math. (Fiftieth Anniversary Issue) vol. 50 (2014) 271-295.
view
22. A Cartan type identity for isoparametric hypersurfaces in symmetric
spaces, Tohoku Math. J. vol. 66 (2014) 435-454. view
23. The constancy of principal curvatures of curvature-adapted submanifolds
in symmetric spaces, Differential Geom. Appl. vol. 35 (2014) 103-113. view
24. Homogeneity of infinite dimensional anti-Kaehler isoparametric submanifolds,
Tokyo J. Math. vol. 37 (2014) 159-178. view
25. Collapse of the mean curvature flow for isoparametric submanifolds
in non-cmpact symmetric spaces, Kodai Math. J. vol. 37 (2014) 355-382.
view
26. Examples of certain kind of minimal orbits of Hermann actions, Hokkaido
Math. J. vol. 43 (2014) 21-42. view
27. Collapse of the mean curvature flow for equifocal submanifolds, Asian
J. Math. vol. 15 (2011) 101-128. view
28. Hermann type actions on a pseudo-Riemannian symmetric space, Tsukuba
J. Math. vol. 34 (2010) 137-172. view
29. On curvature-adapted and proper complex equifocal submanifolds, Kyungpook
Math. J. vol. 50 (2010) 509-536. view
30. Examples of a complex hyperpolar action without singular orbit, Cubo
A Math. J. vol. 12 (2010) 131-147. view
31. The homogeneous slice theorem for the complete complexification of
a proper complex equifocal submanifold, Tokyo J. of Math. vol. 33 (2010)
1-30. view
32. On non-existenceness of equifocal submanifolds with non-flat section,
Asian J. of Math. vol. 12 (2008) 421-442. view
33. A Chevalley type restriction theorem for a proper complex equifocal
submanifold, Kodai Math. J. vol. 30 (2007) 280-296. view
34. Complex hyperpolar actions with a totally geodesic orbit, Osaka J.
Math. vol. 44 (2007) 491-503. view
35. A splitting theorem for proper compex equifocal submanifolds, Tohoku
Math. J. vol. 58 (2006) 393-417. view
36. The variational formulas for the volume function in the equiaffine
geometry, Hokkaido Math. J. vol. 35 (2006) 719-751. view
37. Complex equifocal submanifolds and infinite dimensional anti-Kaehlerian
isoparametric submanifolds, Tokyo J. Math. vol. 28 (2005) 201-247. view
38. Actions of Hermann type and proper complex equifocal submani- folds,
Osaka J. Math. vol. 42 (2005) 599-611. view
39. Blaschke Dupin hypersurfaces and equiaffine tubes, Results Math. vol.
48 (2005) 97-108. view
40. The quadratic slice theorem and the equiaffine tube theorem for equiaffine
Dupin
hypersurfaces, Results Math. vol. 47 (2005) 69-92. view
41. 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
42. Submanifold geometries in a symmetric space of non-compact type and
a pseudo-Hilbert space, Kyushu J. Math, vol. 58 (2004) 167-202. view
43. A generalization of Lelieuvre's formula for equiaffine immersions of
general codimension, Results Math. vol. 43 (2003) 150-155. view
44. 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
45. On focal points of submanifolds in symmetric spaces, SUT J. Math. vol.
39 (2003) 171-181. view
46. On proper Fredholm submanifolds in a Hilbert space arising from submanifolds
in a symmetric space, Japan J. Math. vol. 28 (2002) 61-80. view
47. The total absolute curvature of an equiaffine immersion, Results Math.
vol. 42 (2002) 81-106. view
48. Tubes of non-constant radius in symmetric spaces, Kyushu J. Math. vol.
56 (2002) 267-291. view
49. Equiaffine immersions of general codimension and its transversal volume
element map, Results Math. vol. 39 (2001) 276-291 (with Kouji Takekuma).
view
50. An extrinsic decomposition theorem and a slant tube theorem for a curvature
netted hypersurface, Results Math. vol. 39 (2001) 245-273. view
51. 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
52. Ehresmann connections for a foliated manifold and certain kinds of
rectangles without terminal vertx, Kodai Math. J. vol. 22 (1999) 402-423.
view
53. 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
54. 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
55. Generalized helical immersions, Tsukuba J. Math. vol. 22 (1998) 407-425.
view
56. On proper helices and extrinsic spheres in pseudo-Riemannian geometry,
Tsukuba J. Math. vol. 20 (1996) 263-280. view
57. The decomposition of curvature netted hypersurfaces, Geometriae Dedicata
vol. 54 (1995) 1-11. view
58. Ehresmann connections for a foliation on a manifold with boundry, SUT
J. Math. vol. 30 (1994) 147-158. view
59. On tubes of nonconstant radius, Tsukuba J. Math. vol. 17 (1993) 267-286.
view
60. Totally umbilic orthogonal nets and decomposition theorems, Saitam
Math. J. vol. 10 (1992) 1-20. view
61. Foliations on a Riemannian manifold and Ehresmann connections, Indiana
Univ. Math. J. vol. 40 (1991) 277-292. view
62. Totally umbilic foliations and decomposition theorems, Saitama Math.
J. vol. 8 (1990) 1-18. view
63. Proper isoparametric semi-Riemannian submanifolds in a semi-Riemannian
space form, Tsukuba J. Math. vol. 13 (1989) 131-146. view
64. 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)
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