This article is cited in 1 paper

An Expression for the Riemann Tensor of a Submanifold Given by a System of Equations in a Riemannian Space

Yu. A. Aminov

Kharkiv State University

Abstract: We derive an expression for the Riemann tensor of a submanifold given implicitly by a system of independent equations in a Riemannian space. In particular, we prove a formula for the internal curvature of a two-surface in a three-dimensional Riemannian space. Some applications of the formula are given.

UDC: 517

Received: 20.04.1999

DOI: 10.4213/mzm451

 English version: Mathematical Notes, 2002, 72:5, 595–599

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