Ricci curvature and quasiconformal deformations of a Riemannian manifold
type: Item
instance of: scholarly article
title: Ricci curvature and quasiconformal deformations of a Riemannian manifold
zbMATH Open document ID: 0698.53021
DOI: 10.1007/BF02568486
author: Antoni Pierzchalski
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155463
review text: 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.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 4144868
zbMATH Keywords: quasiconformal deformations
zbMATH Keywords: Ahlfors Laplacian
zbMATH Keywords: spectral properties
zbMATH Keywords: Ricci tensor
Wikidata QID: Q115392008
reviewed by: Liviu Ornea
MaRDI profile type: Publication
cites work: Quasiconformal deformations and mappings in \(\mathbb R^n\)
cites work: Q3756102
cites work: Q3333305
cites work: Ordinary differential equations and quasiconformal mappings
cites work: Q5615235
description: scientific article; zbMATH DE number 4144868