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.
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页数：16
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