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Almost-Bieberbach groups with prime order holonomy

Karel Dekimpe, Wim Malfait (1996)

Fundamenta Mathematicae

The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base.  In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...

Almost-Einstein manifolds with nonnegative isotropic curvature

Harish Seshadri (2010)

Annales de l’institut Fourier

Let ( M , g ) , n ≥ 4 , be a compact simply-connected Riemannian n -manifold with nonnegative isotropic curvature. Given 0 < l ≤ L , we prove that there exists ε = ε ( l , L , n ) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies Ric - s n g ≤ ε then M is diffeomorphic to a symmetric space of compact type.This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature.

A-manifolds on a principal torus bundle over an almost Hodge A-manifold base

Grzegorz Zborowski (2015)

Annales UMCS, Mathematica

An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies ∇XXRic(X,X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds

Amenable hyperbolic groups

Pierre-Emmanuel Caprace, Yves de Cornulier, Nicolas Monod, Romain Tessera (2015)

Journal of the European Mathematical Society

We give a complete characterization of the locally compact groups that are non elementary Gromov-hyperbolic and amenable. They coincide with the class of mapping tori of discrete or continuous one-parameter groups of compacting automorphisms. We moreover give a description of all Gromov-hyperbolic locally compact groups with a cocompact amenable subgroup: modulo a compact normal subgroup, these turn out to be either rank one simple Lie groups, or automorphism groups of semiregular trees acting doubly...

An algorithm based on rolling to generate smooth interpolating curves on ellipsoids

Krzysztof Krakowski, Fátima Silva Leite (2014)

Kybernetika

We present an algorithm to generate a smooth curve interpolating a set of data on an n -dimensional ellipsoid, which is given in closed form. This is inspired by an algorithm based on a rolling and wrapping technique, described in [11] for data on a general manifold embedded in Euclidean space. Since the ellipsoid can be embedded in an Euclidean space, this algorithm can be implemented, at least theoretically. However, one of the basic steps of that algorithm consists in rolling the ellipsoid, over...

An anti-Kählerian Einstein structure on the tangent bundle of a space form

Vasile Oproiu, Neculai Papaghiuc (2005)

Colloquium Mathematicae

In [11] we have considered a family of almost anti-Hermitian structures (G,J) on the tangent bundle TM of a Riemannian manifold (M,g), where the almost complex structure J is a natural lift of g to TM interchanging the vertical and horizontal distributions VTM and HTM and the metric G is a natural lift of g of Sasaki type, with the property of being anti-Hermitian with respect to J. Next, we have studied the conditions under which (TM,G,J) belongs to one of the eight classes of anti-Hermitian structures...

An application of Lie groupoids to a rigidity problem of 2-step nilmanifolds

Hamid-Reza Fanaï, Atefeh Hasan-Zadeh (2019)

Mathematica Bohemica

We study a problem of isometric compact 2-step nilmanifolds M / Γ using some information on their geodesic flows, where M is a simply connected 2-step nilpotent Lie group with a left invariant metric and Γ is a cocompact discrete subgroup of isometries of M . Among various works concerning this problem, we consider the algebraic aspect of it. In fact, isometry groups of simply connected Riemannian manifolds can be characterized in a purely algebraic way, namely by normalizers. So, suitable factorization...

An application of principal bundles to coloring of graphs and hypergraphs

Milgram, James R., Zvengrowski, Peter (1994)

Proceedings of the Winter School "Geometry and Physics"

An interesting connection between the chromatic number of a graph G and the connectivity of an associated simplicial complex N ( G ) , its “neighborhood complex”, was found by Lovász in 1978 (cf. L. Lovász [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a k -uniform hypergraph H , for k an odd prime, using an associated simplicial complex C ( H ) , was found ([N. Alon, P. Frankl and L. Lovász, Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)],...

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