Vol. 34, No. 1, 1970

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ISSN: 0030-8730
Sufficient conditions for a Riemannian manifold to be locally symmetric

Kouei Sekigawa and Shûkichi Tanno

Vol. 34 (1970), No. 1, 157–162
Abstract

In a locally symmetric Riemannian manifold the scalar curvature is constant and each k-th covariant derivative of the Riemannian curvature tensor vanishes. In this note, we show that if the covariant derivatives of the Riemannian curvature tensor satisfy some algebraic conditions at each point, then the Riemannian manifold is locally symmetric.

Mathematical Subject Classification
Primary: 53.73
Milestones
Received: 6 October 1969
Published: 1 July 1970
Authors
Kouei Sekigawa
Shûkichi Tanno