The Obata conjecture for dimension 2
type: Item
instance of: scholarly article
title: The Obata conjecture for dimension 2
zbMATH Open document ID: 1076.53052
published in: Archiv der Mathematik
publication date: 2004-11-26T00:00:00Z
review text: The author confirms a conjecture of M. Obata on Riemannian surfaces (geometric sense) in the following form: Let \( (M^{2},g) \) be a connected compact two-dimensional Riemannian manifold. If the Lie group \( ({\mathbb{R}},+) \) acts on \( (M^{2},g) \) with projective transformations then the metric \( g \) is of constant positive curvature or all transformations are isometries. He announces the generalization of his result to the complete case. A projective transformation of a Riemannian manifold is a diffeomorphism taking geodesics to geodesics ignoring the parametrization.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C24
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 2119264
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: dimension two
zbMATH Keywords: geodesic
zbMATH Keywords: projective transformation
zbMATH Keywords: Obata conjecture
author: Vladimir S. Matveev
reviewed by: Rolf Walter
MaRDI profile type: Publication
full work available at URL: s00013-003-4905-8
OpenAlex ID: W1995167793
DOI: 10.1007/S00013-003-4905-8
description: scientific article; zbMATH DE number 2119264