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Homogeneous Riemannian spaces of negative curvature

D. V. Alekseevskii


Abstract: In this paper the structure of simply-transitive isometry groups of a Riemannian space with nonpositive curvature is studied. The results obtained are then applied to classify Riemannian spaces of negative curvature possessing a metabelian transitive isometry group and also to classify homogeneous Einstein spaces with nonpositive curvature and with dimension $m\leqslant5$.
Bibliography: 13 titles.

UDC: 519.46

MSC: Primary 53C30, 22E20; Secondary 53C25, 22E25, 22E60

Received: 10.04.1974

 English version: Mathematics of the USSR-Sbornik, 1975, 25:1, 87–109

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