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Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes

Alexander I. Bobenko, Ivan Izmestiev (2008)

Annales de l’institut Fourier

We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized convex...

Algebraic analysis of the Rarita-Schwinger system in real dimension three

Alberto Damiano (2006)

Archivum Mathematicum

In this paper we use the explicit description of the Spin– 3 2 Dirac operator in real dimension 3 appeared in (Homma, Y., The Higher Spin Dirac Operators on 3 –Dimensional Manifolds. Tokyo J. Math. 24 (2001), no. 2, 579–596.) to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita–Schwinger operators. We make use of the general theory provided by (Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac systems and computational...

Algebraic representation formulas for null curves in Sl(2,ℂ)

Hubert Gollek (2005)

Banach Center Publications

We study curves in Sl(2,ℂ) whose tangent vectors have vanishing length with respect to the biinvariant conformal metric induced by the Killing form, so-called null curves. We establish differential invariants of them that resemble infinitesimal arc length, curvature and torsion of ordinary curves in Euclidean 3-space. We discuss various differential-algebraic representation formulas for null curves. One of them, a modification of the Bianchi-Small formula, gives an Sl(2,ℂ)-equivariant bijection...

Algebroid nature of the characteristic classes of flat bundles

Jan Kubarski (1998)

Banach Center Publications

The following two homotopic notions are important in many domains of differential geometry: - homotopic homomorphisms between principal bundles (and between other objects), - homotopic subbundles. They play a role, for example, in many fundamental problems of characteristic classes. It turns out that both these notions can be - in a natural way - expressed in the language of Lie algebroids. Moreover, the characteristic homomorphisms of principal bundles (the Chern-Weil homomorphism [K4], or the...

Almost classical solutions of static Stefan type problems involving crystalline curvature

Piotr Bogusław Mucha, Piotr Rybka (2009)

Banach Center Publications

In this note we analyze equilibria of static Stefan type problems with crystalline/singular weighted mean curvature in the plane. Our main goal is to improve the meaning of variational solutions so that their properties allow us to call them almost classical solutions. The idea of our approach is based on a new definition of a composition of multivalued functions.

Almost Contact B-metric Manifoldsas Extensions of a 2-dimensional Space-form

Hristo M. Manev (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The object of investigations are almost contact B-metric manifolds which are derived as a product of a real line and a 2-dimensional manifold equipped with a complex structure and a Norden metric. There are used two different methods for generation of the B-metric on the product manifold. The constructed manifolds are characterised with respect to the Ganchev–Mihova–Gribachev classification and their basic curvature properties.

Almost contact metric submersions and curvature tensors.

Tshikunguila Tshikuna-Matamba (2005)

Extracta Mathematicae

It is known that L. Vanhecke, among other geometers, has studied curvature properties both on almost Hermitian and almost contact metric manifolds.The purpose of this paper is to interrelate these properties within the theory of almost contact metric submersions. So, we examine the following problem: Let f: M → B be an almost contact metric submersion. Suppose that the total space is a C(α)-manifold. What curvature properties do have the fibres or the base space?

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