Ricci curvature and quasiconformal deformations of a Riemannian manifold
The study of quasiconformal deformations on an n-dimensional Riemannian manifold (M,g) leads naturally to the consideration of the Ahlfors Laplacian \(L=S^*S\) where S is the first order differential operator \(SZ={\mathcal L}_ Zg-(2/n)div Z\cdot g\) and \(S^*\) its formal adjoint. The aim of this paper is to establish spectral properties of L using a decomposition formula involving the Ricci tensor. Particularly, lower bounds for the constant of quasi-conformality for normalized deformations on compact Riemannian manifolds with positive definite, negative definite or vanishing Ricci tensor are obtained.
scientific article; zbMATH DE number 4144868