Spectra, rigidity and stability of sine-cones

Abstract

We compute the spectra of the Laplace-Beltrami operator, the connection Laplacian on 1-forms and the Einstein operator on symmetric 2-tensors on the sine-cone over a positive Einstein manifold (M, g). We conclude under which conditions on (M, g), the sine-cone is dynamically stable under the singular Ricci-de Turck flow and rigid as a singular Einstein manifold.

Rigidity of $SU_n$-type symmetric spaces

“…There have also been other interesting developments concerning deformability of Einstein metrics and stability questions. For example, there is recent work by Kröncke on sine-cones [19]. The interaction of rigidity and stability questions with other geometric stuctures (e.g.…”