On the Lichnerovicz Laplacian

S. E. Stepanov ; I. I. Tsyganok

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 67-74.

Résumé

In this paper, we study the geometry of the kernel of the Lichnerovicz Laplacian in the case of complete and, in particular, compact Riemannian manifolds, and also propose a lower estimate of its eigenvalues on a compact Riemannian manifold with the curvature operator bounded from below and an upper estimate of its eigenvalues on a compact Riemannian manifold with the Ricci curvature bounded from below. We define the Lichnerovicz Laplacian on the space of smooth sections of the bundle of covariant tensors as is required by its original definition; this distinguishes our results from results obtained earlier.

Détail

Keywords: Riemannian manifold, covariant tensor, kernel of the Laplacian, eigenvalue of the Laplacian.
Mots-clés : Lichnerovicz Laplacian

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