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.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this paper, it was shown that all nonsingular holomorphic distributions of arbitrary codimension on certain Hopf manifolds are induced by a mononial holomorphic k-form.
Abstract: We classify nonsingular holomorphic distributions of arbitrary codimension on certain Hopf manifolds. We prove that all holomorphic distribution of codimension k on a generic Hopf manifold is induced by a mononial holomorphic k-form.
Posted Content•
TL;DR: In this paper, the authors prove Sard's conjecture for the endpoint map in the case of degenerate Engel distributions, where the set of singular horizontal curves starting from the same point has measure zero: a full 2 dimensional disk.
Abstract: Let D be a rank 2 bracket generating distribution on a 4 manifold, D is Engel if its growth vector is maximal. When this maximality fails the distribution is degenerate. We prove Sard's conjecture for the endpoint map in the case of degenerate Engel distributions. In this case the set of singular horizontal curves starting from the same point has measure zero: a full 2 dimensional disk.
Posted Content•
TL;DR: In this article, a degenerate Ricci-type flow in a screen integrable globally null manifold is introduced via the intrinsic Ricci tensor of the Riemannian leaf.
Abstract: Locally, a screen integrable globally null manifold $M$ splits through a Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$ tangent to its radical distribution. The leaf $M'$ carries a lot of geometric information about $M$ and, in fact, forms a basis for the study of expanding and non-expanding horizons in black hole theory. In the present paper, we introduce a degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor of $M$. Several new gradient estimates regarding the flow are proved.
TL;DR: In this article, the authors studied the geometry of r-lightlike submanifolds M of a semi-Riemannian manifold M of index r and showed that the screen distribution of M is to-tally geodesic in M, and at least one among the r-th lightlike second fundamental forms is parallel with respect to the induced connection of M.
Abstract: . We study the geometry of r-lightlike submanifolds M of asemi-Riemannian manifold M with a semi-symmetric non-metric connec-tion subject to the conditions; (a) the screen distribution of M is to-tally geodesic in M, and (b) at least one among the r-th lightlike secondfundamental forms is parallel with respect to the induced connection ofM. The main result is a classi cation theorem for irrotational r-lightlikesubmanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection. 1. IntroductionThe geometry of lightlike submanifolds is used in mathematical physics, inparticular, in general relativity since lightlike submanifolds produce models ofdi erent types of horizons (event horizons, Cauchy’s horizons, Kruskal’s hori-zons). The universe can be represented as a four dimensional Lorentz subman-ifold (spacetime) embedded in an (n+ 4)-dimensional semi-Riemannian mani-fold. Lightlike hypersurfaces are also studied in the theory of electromagnetism[1]. Thus, large number of applications but limited information available, moti-vated us to do research on this subject matter. Duggal-Bejancu [1] and Kupeli[2] developed the general theory of degenerate (lightlike) submanifolds. Theyconstructed a transversal vector bundle of lightlike submanifold and investi-gated various properties of these manifolds. Duggal-Jin [3] studied totallyumbilical lightlike submanifold of a semi-Riemannian manifold. Ageshe andChae [4] introduced the notion of a semi-symmetric non-metric connection ona Riemannian manifold. Ya˘sar, C˘oken and Yucesan [5] and Jin [6] studied light-like hypersurfaces in semi-Riemannian manifolds admitting a semi-symmetricnon-metric connections. The geometry of half lightlike submanifolds of a semi-Riemannian manifold with semi-symmetric non-metric connection was studied
TL;DR: In this article, the authors studied the distribution of critical circles of a four-dimensional manifold M4 with boundary ∂M4 that satisfies the condition ξ(∂m4)=ξ(M4, ∂m 4)=0 but does not contain any circularm-function.
Abstract: Circularm-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifoldM4 with boundary ∂M4 that satisfies the condition ξ(∂M4)=ξ(M4,∂M4)=0 but does not contain any circularm-function. We prove that a manifold with boundaryMn (n≥5) such that ξ(∂Mn, ∂Mn)=0 always contains a circularm-function without critical points in the interior manifold.