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

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