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 article, the authors consider the Hodge Laplacian for a φ-metric and construct the corresponding heat kernel as a polyhomogeneous conormal distribution on an appropriate manifold with corners.
Abstract: In this paper we continue the analysis of spectral problems in the setting of complete manifolds with fibred boundary metrics, also referred to as $\phi$-metrics, as initiated in our previous work. We consider the Hodge Laplacian for a $\phi$-metric and construct the corresponding heat kernel as a polyhomogeneous conormal distribution on an appropriate manifold with corners. Our discussion is a generalization of an earlier work by Albin and provides a fundamental first step towards analysis of Ray-Singer torsion, eta-invariants and index theorems in the setting.
2 citations
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TL;DR: In this paper, the main notions from the geometry of (almost) contact manifolds in the category of Lie algebroids were generalized to Riemannian Lie alges.
Abstract: In this paper we generalize the main notions from the geometry of (almost) contact manifolds in the category of Lie algebroids. Also, using the framework of generalized geometry, we obtain an (almost) contact Riemannian Lie algebroid structure on a vertical Liouville distribution over the big-tangent manifold of a Riemannain manifold.
2 citations
TL;DR: A sub-Finslerian manifold is a manifold endowed with a Finsler type metric which is defined on a k-dimensional smooth distribution only, not on the whole tangent manifold as mentioned in this paper.
Abstract: A sub-Finslerian manifold is, roughly speaking, a manifold endowed with a Finsler type metric which is defined on a k-dimensional smooth distribution only, not on the whole tangent manifold. Our pu...
2 citations
Posted Content•
TL;DR: In this paper, the distribution of the Frobenius traces on $K3$ surfaces has been studied and the Sato-Tate conjecture has been shown to hold on these surfaces.
Abstract: We study the distribution of the Frobenius traces on $K3$ surfaces. We compare experimental data with the predictions made by the Sato--Tate conjecture, i.e. with the theoretical distributions derived from the theory of Lie groups assuming equidistribution. Our sample consists of generic $K3$ surfaces, as well as of such having real and complex multiplication. We report evidence for the Sato--Tate conjecture for the surfaces considered.
2 citations
Posted Content•
04 Jun 2014
TL;DR: In this article, it was shown that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all germs of holonomy between a fiber and a holomorphic section of the bundle are led to singularities by almost every developed geodesic ray.
Abstract: In this paper we study the problem of analytic extension of germs of holonomy of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is non-elementary and parabolic, all the germs of holonomy between a fiber and a holomorphic section of the bundle are led to singularities by almost every developed geodesic ray. We study in detail the distribution of these singularities and prove in particular that they are included and dense in the limit set and uncountable, giving another negative answer to a conjecture of Loray.
2 citations