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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 1969 Volume 6, Issue 4, Pages 371–380 (Mi mzm6943)

This article is cited in 3 papers

Infinitely small transformations preserving the curvature of a Riemannian space

S. I. Fedishchenko

I. I. Mechnikov Odessa National University

Abstract: The necessary and sufficient conditions for tensor character are obtained, for which an infinitely small transformation of the space $V_n4 preserves its Riemannian curvature for any two-dimensional area. It is proved that for $n>3$ the subprojective spaces of the exceptional case, satisfying a certain condition, and only they, permit nontrivial, infinitely small conformal transformations preserving the Riemannian curvature of each two-dimensional area.

UDC: 513.78

Received: 10.06.1968


 English version:
Mathematical Notes, 1969, 6:4, 680–685

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