Topic
Distribution (differential geometry)
About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.
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TL;DR: In this paper, a light-like hypersurface of indefinite Sasakian manifold, tangent to the structure vector field x, has been studied and sufficient conditions have been given for it to be mixed totally geodesic, D-totally geodesics, D\perp-disparallelism of the distribution T M ∆ of rank 1 (Theorem 4.22) of Theorem 2.2.
Abstract: In this paper, we study a lightlike hypersurface of indefinite Sasakian manifold, tangent to the structure vector field x. Theorems on parallel and Killing distributions are obtained. Necessary and sufficient conditions have been given for lightlike hypersurface to be mixed totally geodesic, D-totally geodesic, D\perp-totally geodesic and D'-totally geodesic. We prove that, if the screen distribution of lightlike hypersurface M of indefinite Sasakian manifold is totally umbilical, the D\perp-geodesibility of M is equivalent to the D\perp-parallelism of the distribution T M\perp of rank 1 (Theorem \ref{Theoscre}). Finally, we give the D\perp-version (Theorem 4.22) of the Theorem 2.2 ([11], page 88).
10 citations
TL;DR: In this paper, it was shown that any two points in such a domain can be joined by a horizontal curve which is piecewise holomorphic, based on Griffiths' horizontal differential system of algebraic geometry and the contact system of classical mechanics.
Abstract: Variations of Hodge structure of weight two are integral manifolds for a distribution in the tangent bundle of a period domain. This distribution has dimension h2 0h 1 and is nonintegrable for h2,0 > 1 . In this case it is known that the dimension of an integral manifold does not exceed 1h2Oh',' . 2 Here we give a new proof, based on an analogy between Griffiths' horizontal differential system of algebraic geometry and the contact system of classical mechanics. We show also that any two points in such a domain can be joined by a horizontal curve which is piecewise holomorphic.
10 citations
TL;DR: Goursat distributions are subbundles, of codimension at least 2, in the tangent bundles to manifolds having the flag of consecutive Lie squares of ranks not depending on a point and growing very slowly as mentioned in this paper.
Abstract: Goursat distributions are subbundles, of codimension at least 2, in the tangent bundles to manifolds having the flag of consecutive Lie squares of ranks not depending on a point and growing—very slowly—always by 1. The length of a flag thus equals the corank of the underlying distribution.
10 citations
TL;DR: In this paper, the Legendre transformation is used to transform a compact m-dimensional connected Riemannian manifold into a C-dimensional configuration space, where the dimension m is the degree of freedom, the tangent bundle 7'44 of M the velocity phase space and the cotangent bundle T*M the momentum phase space.
10 citations
TL;DR: In this article, a variational principle for geodesics on a semi-Riemannian manifold M of arbitrary index k and possessing k linearly independent Killing vector fields that generate a timelike distribution on M was proved.
10 citations