This article is cited in 11 papers

Some generalizations of the Riemann spaces of Einstein

G. M. Kuz'mina

Moscow Engineering Physics Institute

Abstract: We introduce a class of Riemann structures, called generalized Einstein structures of index $2e$, of which Einstein spaces are a particular case. We show that these structures are stationary for functions introduced on a family of Riemann structures of the compact manifold of H. Weyl. This result solves a problem of M. Berger. As examples of structures which are generalized Einstein structures over all indices we cite homogeneous compact Riemann spaces with a nondecomposable isotropy group and products of such spaces.

UDC: 513

Received: 25.05.1973

 English version: Mathematical Notes, 1974, 16:4, 961–963

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