We study the curvature properties of almost Hermitian surfaces with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. Local structure theorems for such almost Hermitian surfaces are provided, and several examples related to these theorems are given.
We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not...
We define a distance between submanifolds of a riemannian manifold and show that, if a compact submanifold is not moved too much under the isometric action of a compact group , there is a -invariant submanifold -close to . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...
In the present paper we have obtained the necessary condition for the existence of almost pseudo symmetric and almost pseudo Ricci symmetric Sasakian manifold admitting a type of quarter symmetric metric connection.
In this paper, we introduce the notion of symplectic harmonic maps between tamed manifolds and establish some properties. In the case where the manifolds are almost Hermitian manifolds, we obtain a new method to contruct harmonic maps with minimal fibres. We finally present examples of such applications between projectives spaces.
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,...
Let , , be a compact simply-connected Riemannian -manifold with nonnegative isotropic curvature. Given , we prove that there exists satisfying the following: If the scalar curvature of satisfiesand the Einstein tensor satisfiesthen 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.
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
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...