Stabilities of affine Legendrian submanifolds and their moduli spaces

被引：3

作者：

Kawai, Kotaro ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2016年 / 47卷

关键词：

Affine Lagrangian submanifolds; Affine Legendrian submanifolds; Stabilities; Moduli spaces; SASAKIAN MANIFOLDS;

D O I：

10.1016/j.difgeo.2016.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of affine Legendrian submanifolds in Sasakian manifolds and define a canonical volume called the phi-volume as odd dimensional analogues of affine Lagrangian (totally real or purely real) geometry. Then we derive the second variation formula of the phi-volume to obtain the stability result in some n-Einstein Sasakian manifolds. It also implies the convexity of the phi-volume functional on the space of affine Legendrian submanifolds. Next, we introduce the notion of special affine Legendrian submanifolds in Sasaki Einstein manifolds as a generalization of that of special Legendrian submanifolds. Then we show that the moduli space of compact connected special affine Legendrian submanifolds is a smooth Frechet manifold. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：159 / 189

页数：31

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