Eigenvalue estimates for a class of elliptic differential operators on compact manifolds

被引：1

作者：

Alencar H. ^{[1
]}

Neto G.S. ^{[1
]}

Zhou D. ^{[2
]}

机构：

[1] Instituto de Matemática, Universidade Federal de Alagoas, Maceió, 57072-900, AL

[2] Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, 24020-140, RJ

来源：

Bulletin of the Brazilian Mathematical Society, New Series | 2015年 / 46卷 / 3期

关键词：

Bochner formula; elliptic operator; first eigenvalue; Riemannian manifolds;

D O I：

10.1007/s00574-015-0102-1

中图分类号：

学科分类号：

摘要：

Themotivation of this paper is to study a second order elliptic operatorwhich appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant r-mean curvature. We prove a generalizedBochner-type formula for such a kind of operators and as applicationswe obtain some sharp estimates for the first nonzero eigenvalues in two special cases. These results can be considered as generalizations of the Lichnerowicz-Obata Theorem. © 2015, Sociedade Brasileira de Matemática.

引用

页码：491 / 514

页数：23

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