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
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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