A practical criterion for some submanifolds to be totally geodesic

被引：2

作者：

Kim, Young Ho ^{[1
]}

Maeda, Sadahiro

机构：

[1] Kyungpook Natl Univ, Coll Nat Sci, Dept Math, Taegu 702701, South Korea

[2] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

来源：

MONATSHEFTE FUR MATHEMATIK | 2006年 / 149卷 / 03期

关键词：

Kahler immersions; totally geodesic immersions; Kahler Frenet curves; Kahler circles; extrinsic hyperspheres;

D O I：

10.1007/s00605-005-0379-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our main theorem is a characterization of a totally geodesic Kahler immersion of a complex n-dimensional Kahler manifold M-n into the arbitrary complex (n + p)-dimensional Kahler manifold Mn+p by observing the extrinsic shape of Kahler Frenet curves on the submanifold M-n. Those curves are closely related to the complex structure of M-n.

引用

页码：233 / 242

页数：10

共 12 条

[1] Characterization of totally umbilic hypersurfaces in a space form by circles
Adachi, T
Maeda, S
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2005, 55 (01) : 203 - 207
[2] ADACHI T, 2006, IN PRESS COLL MATH
[3] ON THE LANDAU-LEVELS ON THE HYPERBOLIC PLANE
COMTET, A
[J]. ANNALS OF PHYSICS, 1987, 173 (01) : 185 - 209
[4] SUB-MANIFOLDS IN EUCLIDEAN-SPACE WITH SIMPLE GEODESICS
FERUS, D
SCHIRRMACHER, S
[J]. MATHEMATISCHE ANNALEN, 1982, 260 (01) : 57 - 62
[5] Geometric meaning of isoparametric hypersurfaces in a real space form
Kimura, M
Maeda, S
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2000, 43 (01): : 74 - 78
[6] Characterizations of geodesic hyperspheres in a complex projective space by observing the extrinsic shape of geodesics
Maeda, S
Ogiue, K
[J]. MATHEMATISCHE ZEITSCHRIFT, 1997, 225 (04) : 537 - 542
[7] REAL HYPERSURFACES OF COMPLEX PROJECTIVE SPACES
MAEDA, S
[J]. MATHEMATISCHE ANNALEN, 1983, 263 (04) : 473 - 478
[8] A characterization of the second Veronese embedding into a complex projective space
Maeda, S
Adachi, T
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2001, 77 (07) : 99 - 102
[9] MAEDA S, 2006, IN PRESS MATH Z
[10] COMPLEX-SPACE FORMS IMMERSED IN COMPLEX-SPACE FORMS
NAKAGAWA, H
OGIUE, K
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 219 (MAY) : 289 - 297

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