On the curvature of the diffeomorphism group
type: Item
instance of: scholarly article
title: On the curvature of the diffeomorphism group
zbMATH Open document ID: 0816.58009
DOI: 10.1007/BF00773452
author: Alexander M. Lukatsky
published in: Annals of Global Analysis and Geometry
publication date: 1995-03-01T00:00:00Z
review text: Let \(\text{SDIFF}(M)\) denote the group of diffeomorphisms preserving Riemannian density on a closed manifold \(M\). Using the results of \textit{V. I. Arnol'd} [Ann. Inst. Fourier 16, 319--361 (1966; Zbl 0148.45301)] the author obtains an expression for the sectional curvature of \(\text{SDIFF}(M)\) and establishes its negativeness for locally Euclidean \(M\).
Mathematics Subject Classification ID: 58D05
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 727085
zbMATH Keywords: closed manifold
zbMATH Keywords: vector field
zbMATH Keywords: Riemannian metric
zbMATH Keywords: instability
zbMATH Keywords: ideal incompressible fluid
zbMATH Keywords: group of diffeomorphisms
zbMATH Keywords: sectional curvature
reviewed by: Witold Mozgawa
MaRDI profile type: Publication
cites work: Groups of diffeomorphisms and the motion of an incompressible fluid
cites work: Q3897665
description: scientific article; zbMATH DE number 727085