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- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Sociedade Brasileira de Matemática
- Subject
- Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-015-0102-1
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Oct 3, 2015