On minimal Legendrian submanifolds of Sasaki-Einstein manifolds

被引：1

作者：

Calamai, Simone ^{[1
]}

Petrecca, David ^{[2
]}

机构：

[1] Univ Florence, Dipartimento Matemat & Informat Ulisse Dini, Florence, Italy

[2] Univ Pisa, Dipartimento Matemat, Pisa, Italy

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2014年 / 25卷 / 09期

关键词：

Sasaki-Einstein manifold; Legendrian submanifolds; minimal submanifolds; totally geodesic submanifolds; Laplacian eigenfunctions; contact moment map; Nomizu operator;

D O I：

10.1142/S0129167X14500839

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a given minimal Legendrian submanifold L of a Sasaki-Einstein manifold we construct two families of eigenfunctions of the Laplacian of L and we give a lower bound for the dimension of the corresponding eigenspace. Moreover, in the case the lower bound is attained, we prove that L is totally geodesic and a rigidity result about the ambient manifold. This is a generalization of a result for the standard Sasakian sphere done by Le and Wang.

引用

页数：16

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