Accession Number:

AD0263313

Title:

ON A THEOREM OF YANO AND NAGANO

Descriptive Note:

Corporate Author:

WAYNE STATE UNIV DETROIT MICH

Personal Author(s):

Report Date:

1961-07-01

Pagination or Media Count:

1.0

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

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE