A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces

被引：3

作者：

Hashinaga, Takahiro ^{[1
]}

Kajigaya, Toru ^{[2
]}

机构：

[1] Kitakyushu Coll, Natl Inst Technol, Kokuraminami Ku, 5-20-1 Shii, Kitakyushu, Fukuoka 8020985, Japan

[2] Osaka City Univ, Adv Math Inst, Sumiyoshi Ku, Osaka 5588585, Japan

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2017年 / 51卷 / 01期

关键词：

Homogeneous Lagrangian submanifolds; Complex hyperbolic spaces; ISOPARAMETRIC HYPERSURFACES;

D O I：

10.1007/s10455-016-9521-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study homogeneous Lagrangian submanifolds in complex hyperbolic spaces. We show there exists a correspondence between compact homogeneous Lagrangian submanifolds in and the ones in , or equivalently, in . Furthermore, we construct and classify non-compact homogeneous Lagrangian submanifolds in obtained by the actions of connected closed subgroups of the solvable part of the Iwasawa decomposition.

引用

页码：21 / 33

页数：13

共 18 条

[1] Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces
Amarzaya, A
Ohnita, Y
[J]. TOHOKU MATHEMATICAL JOURNAL, 2003, 55 (04) : 583 - 610
[2] [Anonymous], 1995, LECT NOTES MATH
[3] [Anonymous], 1999, OXFORD MATH MONOGRAP
[4] Audin M., 1991, PROGR MATH, V93
[5] Homogeneous Lagrangian submanifolds
Bedulli, Lucio
Gori, Anna
[J]. COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2008, 16 (03) : 591 - 615
[6] Cohomogeneity one actions on symmetric spaces of noncompact type
Berndt, Juergen
Tamaru, Hiroshi
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2013, 683 : 129 - 159
[7] Berndt J, 2012, COMMUN ANAL GEOM, V20, P435
[8] Deltour G, 2013, J DIFFER GEOM, V93, P379
[9] HOMOGENEOUS ISOPARAMETRIC HYPERSURFACES IN SPHERES WITH FOUR DISTINCT PRINCIPAL CURVATURES AND MOMENT MAPS
Fujii, Shinobu
[J]. TOHOKU MATHEMATICAL JOURNAL, 2010, 62 (02) : 191 - 213
[10] Helgason S., 1962, Differential Geometry and Symmetric Spaces

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