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
收藏
页码：159 / 189
页数：31
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