小池直之研究室 Naoyuki Koike Laboratory

著書・論文

Books & Publications

著書

Books
位相空間の道標
− 基礎から位相不変量まで −
共立出版・2025年4月3日発売・280ページ・ISBN 978-4-320-11576-7

Signpost of Topological Space — From Foundation to Topological Invariants

出版社サイトへ
積分公式で啓くベクトル解析と微分幾何学
− ストークスの定理から変分公式まで −
共立出版・2022年9月12日出版・385ページ（2023年5月 初版第2刷）・ISBN 978-4-320-11475-3

Vector Analysis & Differential Geometry Enlightened by Integral Formulas — From Stokes' Theorem to Variational Formula

出版社サイトへ 正誤表（出版社サイト「関連情報」）
理論物理に潜む部分多様体幾何
− 一般相対性理論・ゲージ理論との関わり −
共立出版・2021年3月9日出版・438ページ（2025年5月 初版第3刷）・ISBN 978-4-320-11440-1

擬リーマン部分多様体論、リー群作用の軌道幾何、対称空間論に関する入門書であり、発展的内容やゲージ理論と関わる無限次元部分多様体についても述べた自信作。対称空間論をはじめて学ぶ方に特にお勧めです。

出版社サイトへ 初版第2刷の正誤表（出版社サイト「関連情報」） 訂正箇所ファイル
平均曲率流
− 部分多様体の時間発展 −
共立出版・2019年4月10日出版・376ページ（2020年5月 初版第2刷）・ISBN 978-4-320-11376-3

Mean curvature flow — Time evolution of submanifolds

出版社サイトへ

共著：理工系の基礎 数学 II（丸善出版・2018年・208ページ・ISBN 978-4-621-30250-7）。全著者名（担当したページの順）：小池直之，山川大亮，金子宏，黒沢健，宮岡悦良，瀬尾隆，石渡恵美子，相原研輔，関川浩，周冠宇

『理論物理に潜む部分多様体幾何』訂正箇所ファイル

P.1 P.35 P.36 P.117 P.160 P.163 P.164 P.188 P.202 P.216

『積分公式で啓くベクトル解析と微分幾何学』の正誤表は共立出版のサイト（「関連情報」をクリック）にあります。

査読付き論文

Refereed Papers
  1. Isotropy invariant graphical mean curvature flows in warped products, J. Geom. Anal. vol. 35, (2025) 24pages. (with Naotoshi Fujihara) view
  2. Translators invariant under hyperpolar actions, Kodai Math. J. vol. 48, (2025) 101-122. (with Tomoki Fujii)view
  3. Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory, Calc. Var. Partial Differential Equations vol. 63, (2024) 56pages.view
  4. Isoparametric submanifolds in Hilbert spaces and holonomy maps, Illinois Journal of Mathematics, vol. 67 (2023) 153-170.view
  5. The preservability of the curvature-adaptedness along the mean curvature flow, Differential Geometry and its Applications vol. 84 (2022) 101931 (15 pages).view
  6. 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
  7. Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space, Math. Nachrichten vol. 293 (2020) 923-944. (with Honoka Kobayashi)view
  8. Isoparametric submanifolds admitting a reflective focal submanifold in symmetric spaces of non-compact type, Osaka J. Math. vol. 57 (2020) 207-246.view
  9. Calabi-Yau structures and special Lagrangian submanifolds of complexified symmetric spaces, Illinois J. Math. vol. 63 (2019) 575-600.view
  10. Equifocal submanifolds in a symmetric space and the infinite dimensional geometry, SUGAKU EXPOSITIONS, vol. 32 (2019) 25-56.view
  11. Mean curvature flow of certain kind of isoparametric foliations on non-compact symmetric spaces, CUBO A Mathematical Journal vol. 20 (2018) 13-30.view
  12. A modified mean curvature flow in Euclidean space and soap bubbles in symmetric spaces, Geometriae Dedicata vol. 195 (2018) 1-17. view
  13. Gauss maps of the Ricci-mean curvature flow, Geometriae Dedicata vol. 194 (2018) 169-185. (with Hikaru Yamamoto)view
  14. 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
  15. Homogeneity of infinite dimensional anti-Kaehler isoparametric submanifolds II, Tokyo J. Math. vol. 40 (2017) 301-337.view
  16. 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
  17. A holonomy invariant anisotropic surface energy in a Riemannian manifold, Differential Geom. Appl. vol. 44 (2016) 98-121.view
  18. 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
  19. On the indices of minimal orbits of Hermann actions, Hokkaido Math. J. vol. 44 (2015) 251-275.view
  20. 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
  21. 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
  22. 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
  23. The complexifications of pseudo-Riemannian manifolds and anti-Kaehler geometry, SUT J. Math. (Fiftieth Anniversary Issue) vol. 50 (2014) 271-295.view
  24. A Cartan type identity for isoparametric hypersurfaces in symmetric spaces, Tohoku Math. J. vol. 66 (2014) 435-454.view
  25. The constancy of principal curvatures of curvature-adapted submanifolds in symmetric spaces, Differential Geom. Appl. vol. 35 (2014) 103-113. view
  26. Homogeneity of infinite dimensional anti-Kaehler isoparametric submanifolds, Tokyo J. Math. vol. 37 (2014) 159-178.view
  27. Collapse of the mean curvature flow for isoparametric submanifolds in non-compact symmetric spaces, Kodai Math. J. vol. 37 (2014) 355-382.view
  28. Examples of certain kind of minimal orbits of Hermann actions, Hokkaido Math. J. vol. 43 (2014) 21-42.view
  29. Collapse of the mean curvature flow for equifocal submanifolds, Asian J. Math. vol. 15 (2011) 101-128.view
  30. Hermann type actions on a pseudo-Riemannian symmetric space, Tsukuba J. Math. vol. 34 (2010) 137-172.view
  31. On curvature-adapted and proper complex equifocal submanifolds, Kyungpook Math. J. vol. 50 (2010) 509-536.view
  32. Examples of a complex hyperpolar action without singular orbit, Cubo A Math. J. vol. 12 (2010) 131-147.view
  33. The homogeneous slice theorem for the complete complexification of a proper complex equifocal submanifold, Tokyo J. of Math. vol. 33 (2010) 1-30.view
  34. On non-existenceness of equifocal submanifolds with non-flat section, Asian J. of Math. vol. 12 (2008) 421-442.view
  35. A Chevalley type restriction theorem for a proper complex equifocal submanifold, Kodai Math. J. vol. 30 (2007) 280-296.view
  36. Complex hyperpolar actions with a totally geodesic orbit, Osaka J. Math. vol. 44 (2007) 491-503.view
  37. A splitting theorem for proper complex equifocal submanifolds, Tohoku Math. J. vol. 58 (2006) 393-417.view
  38. The variational formulas for the volume function in the equiaffine geometry, Hokkaido Math. J. vol. 35 (2006) 719-751.view
  39. Complex equifocal submanifolds and infinite dimensional anti-Kaehlerian isoparametric submanifolds, Tokyo J. Math. vol. 28 (2005) 201-247.view
  40. Actions of Hermann type and proper complex equifocal submanifolds, Osaka J. Math. vol. 42 (2005) 599-611.view
  41. Blaschke Dupin hypersurfaces and equiaffine tubes, Results Math. vol. 48 (2005) 97-108.view
  42. The quadratic slice theorem and the equiaffine tube theorem for equiaffine Dupin hypersurfaces, Results Math. vol. 47 (2005) 69-92.view
  43. 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
  44. Submanifold geometries in a symmetric space of non-compact type and a pseudo-Hilbert space, Kyushu J. Math. vol. 58 (2004) 167-202.view
  45. A generalization of Lelieuvre's formula for equiaffine immersions of general codimension, Results Math. vol. 43 (2003) 150-155.view
  46. 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
  47. On focal points of submanifolds in symmetric spaces, SUT J. Math. vol. 39 (2003) 171-181.view
  48. On proper Fredholm submanifolds in a Hilbert space arising from submanifolds in a symmetric space, Japan J. Math. vol. 28 (2002) 61-80.view
  49. The total absolute curvature of an equiaffine immersion, Results Math. vol. 42 (2002) 81-106.view
  50. Tubes of non-constant radius in symmetric spaces, Kyushu J. Math. vol. 56 (2002) 267-291.view
  51. Equiaffine immersions of general codimension and its transversal volume element map, Results Math. vol. 39 (2001) 276-291. (with Kouji Takekuma)view
  52. An extrinsic decomposition theorem and a slant tube theorem for a curvature netted hypersurface, Results Math. vol. 39 (2001) 245-273.view
  53. The Lipschitz-Killing curvature for an equiaffine immersion and theorems of Gauss-Bonnet type and Chern-Lashof type, Results Math. vol. 39 (2001) 230-244.view
  54. Ehresmann connections for a foliated manifold and certain kinds of rectangles without terminal vertex, Kodai Math. J. vol. 22 (1999) 402-423.view
  55. 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
  56. 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
  57. Generalized helical immersions, Tsukuba J. Math. vol. 22 (1998) 407-425.view
  58. On proper helices and extrinsic spheres in pseudo-Riemannian geometry, Tsukuba J. Math. vol. 20 (1996) 263-280.view
  59. The decomposition of curvature netted hypersurfaces, Geometriae Dedicata vol. 54 (1995) 1-11. view
  60. Ehresmann connections for a foliation on a manifold with boundary, SUT J. Math. vol. 30 (1994) 147-158.view
  61. On tubes of nonconstant radius, Tsukuba J. Math. vol. 17 (1993) 267-286.view
  62. Totally umbilic orthogonal nets and decomposition theorems, Saitama Math. J. vol. 10 (1992) 1-20.view
  63. Foliations on a Riemannian manifold and Ehresmann connections, Indiana Univ. Math. J. vol. 40 (1991) 277-292.view
  64. Totally umbilic foliations and decomposition theorems, Saitama Math. J. vol. 8 (1990) 1-18.view
  65. Proper isoparametric semi-Riemannian submanifolds in a semi-Riemannian space form, Tsukuba J. Math. vol. 13 (1989) 131-146.view
  66. Congruence theorem for proper semi-Riemannian hypersurfaces in a real space form, Yokohama Math. J. vol. 35 (1987) 123-136.view

過去の掲載論文のすべてについては MathSciNet、未掲載の最近の論文については arXiv をご覧ください。