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Sibirskii Matematicheskii Zhurnal, 2001, Volume 42, Number 6, Pages 1340–1349 (Mi smj1391)  
The generalized axiom of spheres

S. I. Okrut

V. N. Karazin Kharkiv National University
Full-text PDF (204 kB)
Abstract: Some generalization is proposed for the axiom of spheres. A collection of Riemannian spaces is constructed which satisfy the generalized axiom of spheres, but do not satisfy the earlier-known axioms of submanifolds. The structure is found of the curvature tensor of manifolds satisfying the generalized axiom of spheres. This structure mostly resembles the structure of the curvature tensor of manifolds with the generalized axiom of planes.
Received: 05.06.2000
Revised: 02.10.2000
English version:
Siberian Mathematical Journal, 2001, Volume 42, Issue 6, Pages 1115–1122
DOI: https://doi.org/10.1023/A:1012848711795
Bibliographic databases:
UDC: 514.76
Language: Russian
Citation: S. I. Okrut, “The generalized axiom of spheres”, Sibirsk. Mat. Zh., 42:6 (2001), 1340–1349; Siberian Math. J., 42:6 (2001), 1115–1122
Citation in format AMSBIB
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\paper The generalized axiom of spheres
\jour Sibirsk. Mat. Zh.
\yr 2001
\vol 42
\issue 6
\pages 1340--1349
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1876820}
\transl
\jour Siberian Math. J.
\yr 2001
\vol 42
\issue 6
\pages 1115--1122
\crossref{https://doi.org/10.1023/A:1012848711795}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000172981200010}
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