Geodesic
The Riemannian manifolds with an axiom of hyperspheres
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001), pp. 392-418.

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The generalization of an axiom of spheres is proposed. It is shown, that the set of the Riemannian spaces satisfying to a proposed axiom, is wider set of spaces satisfying to a generalized axiom of planes. It is found structure of a tensor of a curvature of manifolds with a generalized axiom of spheres. It is found also structure of the Riemannian metric of manifolds, satisfying to generalized axiom of spheres at some natural additional conditions. It is given expression of the Riemannian metric of space with an axiom of $l$-hyperspheres without the additional conditions at rather large $l$. 
@article{JMAG_2001_8_a3,
     author = {S. I. Okrut},
     title = {The {Riemannian} manifolds with an axiom of hyperspheres},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {392--418},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_a3/}
}
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S. I. Okrut. The Riemannian manifolds with an axiom of hyperspheres. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001), pp. 392-418. http://geodesic.mathdoc.fr/item/JMAG_2001_8_a3/