Vol. 25, No. 2, 1968

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ISSN: 0030-8730
A Riemannian space with strictly positive sectional curvature

Grigorios Tsagas

Vol. 25 (1968), No. 2, 381–391
Abstract

Let M1 and M2 be two Riemannian spaces1 with Riemannian metrics d1 and d2 respectively whose sectional curvature is positive constant. We consider the product of the two Riemannian spaces M1 × M2, then the Riemannian space M1 × M2 has nonnegative sectional curvature with respect to the Riemannian metric d1 × d2 but not strictly positive sectional curvature.

We can construct a Riemannian metric on M1 × M2 which approaches the Riemannian metric d1 × d2 as closely as we wish and which has strictly positive sectional curvature.

Mathematical Subject Classification
Primary: 53.72
Milestones
Received: 14 March 1967
Published: 1 May 1968
Authors
Grigorios Tsagas