Connection on the Group of Diffeomorphisms as a Bundle Over the Space of Functions

Jacobian determines a bundle with total space consisting of orientation-preserving diffeomorphisms of a (connected) manifold over the space of positive functions on this manifold (with integral equal to volume for a compact manifold). It is proved that, for the -sphere with standard metric, there is...

Full description

Saved in:
Bibliographic Details
Published in:Functional analysis and its applications 2021-07, Vol.55 (3), p.242-244
Main Author: Gusein-Zade, S. M.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Analysis
Functional Analysis
Isomorphism
Manifolds
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Jacobian determines a bundle with total space consisting of orientation-preserving diffeomorphisms of a (connected) manifold over the space of positive functions on this manifold (with integral equal to volume for a compact manifold). It is proved that, for the -sphere with standard metric, there is a unique connection on this bundle that is invariant with respect to all isometries of the sphere, and a description of this connection is given.
ISSN:0016-2663
1573-8485
DOI:10.1134/S0016266321030072