Deformations of isotropic submanifolds in Kähler manifolds

Bang yen Chen; Jean-Marie Morvan

doi:10.1016/0393-0440(94)90061-2

Deformations of isotropic submanifolds in Kähler manifolds

Bang yen Chen^*, Jean-Marie Morvan

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We study the first and second variations of isotropic submanifolds which preserve the isotropy. In order to do so, we introduce the notions of harmonic, exact and isotropic variations and investigate basic properties of isotropic submanifolds which are minimal under such deformations. Many results in this respect are then obtained. In particular, we obtain a new characterization of Maslov class in terms of such deformations.

Original language	English (US)
Pages (from-to)	79-104
Number of pages	26
Journal	Journal of Geometry and Physics
Volume	13
Issue number	1
DOIs	https://doi.org/10.1016/0393-0440(94)90061-2
State	Published - Jan 1 1994

Keywords

1991 MSC: 53 C 40
53 B 25
58 E 99
58 F 05
Kähler manifolds
deformations
submanifolds

ASJC Scopus subject areas

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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10.1016/0393-0440(94)90061-2

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title = "Deformations of isotropic submanifolds in K{\"a}hler manifolds",

abstract = "We study the first and second variations of isotropic submanifolds which preserve the isotropy. In order to do so, we introduce the notions of harmonic, exact and isotropic variations and investigate basic properties of isotropic submanifolds which are minimal under such deformations. Many results in this respect are then obtained. In particular, we obtain a new characterization of Maslov class in terms of such deformations.",

keywords = "1991 MSC: 53 C 40, 53 B 25, 58 E 99, 58 F 05, K{\"a}hler manifolds, deformations, submanifolds",

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AU - Morvan, Jean-Marie

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N2 - We study the first and second variations of isotropic submanifolds which preserve the isotropy. In order to do so, we introduce the notions of harmonic, exact and isotropic variations and investigate basic properties of isotropic submanifolds which are minimal under such deformations. Many results in this respect are then obtained. In particular, we obtain a new characterization of Maslov class in terms of such deformations.

AB - We study the first and second variations of isotropic submanifolds which preserve the isotropy. In order to do so, we introduce the notions of harmonic, exact and isotropic variations and investigate basic properties of isotropic submanifolds which are minimal under such deformations. Many results in this respect are then obtained. In particular, we obtain a new characterization of Maslov class in terms of such deformations.

KW - 1991 MSC: 53 C 40

KW - 53 B 25

KW - 58 E 99

KW - 58 F 05

KW - Kähler manifolds

KW - deformations

KW - submanifolds

UR - http://www.scopus.com/inward/record.url?scp=38149144738&partnerID=8YFLogxK

U2 - 10.1016/0393-0440(94)90061-2

DO - 10.1016/0393-0440(94)90061-2

M3 - Article

AN - SCOPUS:38149144738

VL - 13

SP - 79

EP - 104

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 1

ER -

Deformations of isotropic submanifolds in Kähler manifolds

Abstract

Keywords

ASJC Scopus subject areas

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