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

Vladimir Rovenski, Sergey Stepanov and Josef Mikeš ()
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Vladimir Rovenski: Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
Sergey Stepanov: Department of Mathematics, Finance University, Leningradsky Prospect, 49–55, 125468 Moscow, Russia
Josef Mikeš: Department of Algebra and Geometry, Faculty of Science, Palacky University, 771 46 Olomouc, Czech Republic

Mathematics, 2023, vol. 11, issue 21, 1-10

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.

Keywords: Lichnerowicz Laplacian; symmetric two-tensors; vanishing theorem; eigenvalue; infinitesimal Einstein deformations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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