ON A THEOREM OF YANO AND NAGANO
Abstract
A complete, connected Einstein space of dimension m greater than 2 on which there exists a vector field generating globally a one-parameter group of non-homothetic transformations is homeomorphic with the m-sphere. This statement is valid for any complete, connected Riemannian manifold if it were known for a manifold of (positive) constant scalar curvature. Evidence is presented strengthening this conjecture. It is shown that if M is a compact Riemannian manifold which is not a homology sphere, then an infinitesimal conformal transformation of M is an infinitesimal isometry. In particular, if a compact, simply connected symmetric space of a connected Lie group admits a non-homothetic transformation (belonging to the connected component of the group of conformal transformations of M) then M is isometric with the m-sphere. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1961
- Accession Number
- AD0263313
Entities
People
- S.i. Goldberg
Organizations
- Wayne State University