A Note on the Geometry of Certain Classes of Lichnerowicz Laplacians and Their Applications-Reference-Cited by-同舟云学术

A Note on the Geometry of Certain Classes of Lichnerowicz Laplacians and Their Applications

Published:2023-10-26 Issue:21 Volume:11 Page:4434
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Rovenski Vladimir¹^ORCID,Stepanov Sergey²^ORCID,Mikeš Josef³^ORCID

Affiliation:

1. Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

2. Department of Mathematics, Finance University, Leningradsky Prospect, 49–55, 125468 Moscow, Russia

3. Department of Algebra and Geometry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic

Abstract

In the present paper, we prove vanishing theorems for the null space of the Lichnerowicz Laplacian acting on symmetric two tensors on complete and closed Riemannian manifolds and further estimate its lowest eigenvalue on closed Riemannian manifolds. In addition, we give an application of the obtained results to the theory of infinitesimal Einstein deformations.

Funder

Palacky University in Olomouc

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/21/4434/pdf

Reference21 articles.

1. Propagateurs et commutateurs en relativité generate;Lichnerowicz;Publ. Math. de l’IHÉS,1961

2. Wu, H.-H. (2017). The Bochner Technique in Differential Geometry, Higher Education Press. CTM, 6.

3. Petersen, P. (2016). Riemannian Geometry, Springer.

4. Pigola, S., Rigoli, M., and Setti, A.G. (2008). Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique, Birkhäuser.

5. Some decomposition of the space of symmetric tensors of a Riemannian manifold;Berger;J. Differ. Geom.,1969