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Mat. Zametki, 1969, Volume 6, Issue 4, Pages 371–380 (Mi mz6943)  

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.

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

Bibliographic databases:

UDC: 513.78
Received: 10.06.1968

Citation: S. I. Fedishchenko, “Infinitely small transformations preserving the curvature of a Riemannian space”, Mat. Zametki, 6:4 (1969), 371–380; Math. Notes, 6:4 (1969), 680–685

Citation in format AMSBIB
\Bibitem{Fed69}
\by S.~I.~Fedishchenko
\paper Infinitely small transformations preserving the curvature of a~Riemannian space
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 371--380
\mathnet{http://mi.mathnet.ru/mz6943}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=256301}
\zmath{https://zbmath.org/?q=an:0189.52501}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 680--685
\crossref{https://doi.org/10.1007/BF01093801}


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