Geodesic webs of hypersurfaces

Document Type

Article

Publication Date

4-1-2009

Abstract

Geometric structures associated with webs of hypersurfaces are studied and geodesic web on an n-dimensional manifold is proved to be associated with a unique projective structure. A d-web is proved to be a geodesic for particular forms depending on basis of vector fields that is dual to the cobasis. The conditions for the (n +2)th foliation to be totally geodesic can be used to determine the skewsymmetric part of webs. A defined set of basis invariants shows that a d-web of hypersurfaces is geodesic. A d-web is found to be locally linearizable if and only if it is geodesic and the Liouville tensor of the canonical projective structure vanishes. Any mapping of a geodesic d-web to another geodesic d-web is found to be a collineation with respect to canonical projective structures. It is also shown that the mapping of distinguished geodesic d-webs is affine with respect to canonical affine structures.

Identifier

65149086103 (Scopus)

Publication Title

Doklady Mathematics

External Full Text Location

https://doi.org/10.1134/S1064562409020355

ISSN

10645624

First Page

284

Last Page

286

Issue

2

Volume

79

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