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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 article, it was shown that given a conformal structure whose holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is always a local metric in the conformal class off a singular set which is Ricci-isotropic and gives rise to a parallel, totally light-like distribution on the tangent bundle.
Abstract: We show that given a conformal structure whose holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is always a local metric in the conformal class off a singular set which is Ricci-isotropic and gives rise to a parallel, totally lightlike distribution on the tangent bundle. This naturally applies to parallel spin tractors resp. twistor spinors on conformal spin manifolds and clarifies which twistor spinors are locally equivalent to parallel spinors. Moreover, we study the zero set of a twistor spinor using the curved orbit decomposition for parabolic geometries. We can completely describe its local structure, construct a natural projective structure on it, and show that locally every twistor spinor with zero is equivalent to a parallel spinor off the zero set. An application of these results in low-dimensional split-signatures leads to a complete geometric description of local geometries admitting non-generic twistor spinors in signatures (3,2) and (3,3) which complements the well-known description of the generic case.

7 citations

Posted Content
TL;DR: In this article, the curvature of a Finsler manifold with corresponding cur-vature tensor is considered and the curvatures of the tangent spaces of the manifold are defined as foliations of the curva-ture operator.
Abstract: Here, a Finsler manifold (M,F) is considered with corresponding cur-vature tensor, regarded as 2-forms on the bundle of non-zero tangentvectors. Certain subspaces of the tangent spaces of M determined bythe curvature are introduced and called k-nullity foliations of the curva-ture operator. It is shown that if the dimension of foliation is constantthen the distribution is involutive and each maximal integral manifold istotally geodesic. Characterization of the k-nullity foliation is given, aswell as some results concerning constancy of the flag curvature, and com-pleteness of their integral manifolds, providing completeness of (M,F).The introduced k-nullity space is a natural extension of nullity space inRiemannian geometry, introduced by S. S. Chern and N. H. Kuiper andenlarged to Finsler setting by H. Akbar-Zadeh and contains it as a specialcase.Keywords: Foliation, k-nullity, Finsler manifolds, Curvature operator.MSC: 2000 Mathematics subject Classification: 58B20, 53C60, 53C12.

7 citations

Journal Article
TL;DR: In this article, the geometry of Einstein half light like submanifolds M of a Lorentz manifold ((c), ) of constant curvature c, equipped with an integrable screen distribution on M such that the induced connection is a metric connection and the operator is a screen shape operator, is studied.
Abstract: In this paper we study the geometry of Einstein half light like submanifolds M of a Lorentz manifold ((c), ) of constant curvature c, equipped with an integrable screen distribution on M such that the induced connection is a metric connection and the operator is a screen shape operator.

7 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that every e-contact manifold that is also K-contact and η-Einstein is a vacuum solution to the most general quadratic-curvature gravity action, in particular of New Massive Gravity.

7 citations

Journal Article
TL;DR: In this article, a Finsler manifold (M,F) is considered with cor- responding curvature tensor, regarded as 2-forms on the bundle of non-zero tangent vectors.
Abstract: Here, a Finsler manifold (M,F) is considered with cor- responding curvature tensor, regarded as 2-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of M determined by the curvature are introduced and called k- nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive and each maximal integral manifold is totally geodesic. Character- ization of the k-nullity foliation is given, as well as some results concerning constancy of the flag curvature, and completeness of their integral manifolds, providing completeness of (M,F). The introduced k-nullity space is a natural extension of nullity space in Riemannian geometry, introduced by Chern and Kuiper and en- larged to Finsler setting by Akbar-Zadeh and contains it as a special case.

7 citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202159
202067
201953
201843
201733