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In the present paper we define Samuelsons webs and their rank. The main result of the paper is the proof that the rank of the Samuelson webs does not exceed 6, as well as finding the conditions under which this rank is maximal for the general Samuelson webs as well as for their singular cases.
The authors found necessary and sufficient conditions for Samuelsons web to be of maximum rank.
In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n+2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provided that one of web
This paper has been withdrawn by the authors due to the fact that the webs considered in the paper are ``Veronese-like webs which are different from Veronese webs.
We find necessary and sufficient conditions for the foliation defined by level sets of a function f(x_{1},...,x_{n}) to be totally geodesic in a torsion-free connection and apply them to find the conditions for d-webs of hypersurfaces to be geodesic,
We present a complete description of a class of linearizable planar geodesic webs which contain a parallelizable 3-subweb.