Conformal immersions of complete Riemannian manifolds and extensions of the Schwarz lemma
type: Item
instance of: scholarly article
title: Conformal immersions of complete Riemannian manifolds and extensions of the Schwarz lemma
zbMATH Open document ID: 0813.53038
DOI: 10.1215/S0012-7094-94-07411-5
author: Andrea Ratto
author: M. Rigoli
author: Laurent Véron
published in: Duke Mathematical Journal
publication date: 1995-05-28T00:00:00Z
review text: A conformal immersion \(\varphi: M\to N\) of a complete connected non-compact Riemannian manifold \((M,g)\) \((m=\dim M\geq 3)\) into another Riemannian manifold \((N,h)\) is weakly distance decreasing (w.d.d.) when \(\varphi^* h= u^{4/ (m-2)} g\) and \(0< u(x) \leq 1\) for all \(x\in M\). The authors provide some conditions on the curvatures of \(M\) and \(N\) which ensure that any conformal immersion \(\varphi\) such that \(s_ N (\varphi (x))\leq s_ M(x)\) \((x\in M)\) is w.d.d. Here, \(s_ M\) and \(s_ N\) are the scalar curvatures of \(M\) and \(N\), respectively.
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 624878
zbMATH Keywords: conformal immersion
zbMATH Keywords: weakly distance decreasing
reviewed by: Paweł Walczak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 624878