This article is cited in 3 papers

An extremal theorem of Riemannian geometry

S. V. Buyalo

Leningrad State University

Abstract: An exact upper estimate for the volume of a tubular neighborhood of a smooth submanifold $N$ of a complete Riemann space $M$ depending upon the volume of $N$ and lower bound for the sectional curvatures of $M$ is given. If $N$ is a closed geodesic, then the equality is attained in the estimate if and only if $M$ is a generalized lens space.

UDC: 513.8

Received: 31.03.1975

 English version: Mathematical Notes, 1976, 19:5, 468–473

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