Download or read book Naturally Reductive Metrics and Einstein Metrics on Compact Lie Groups written by J. E. D'Atri and published by American Mathematical Soc.. This book was released on 1979 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this paper constructs a class of naturally reductive metrics on compact Lie groups and shows that all naturally reductive left invariant metrics are of this type if the group is simple. The second part analyzes the question of when these metrics are Einstein and gives many new examples. In doing this, certain facts are established about the ratios of the Killing forms of a Lie algebra and a subalgebra. Finally, some results are obtained for noncompact groups and more general compact homogeneous spaces.