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A contact metric manifold satisfying a certain curvature condition

Jong Taek Cho (1995)

Archivum Mathematicum

In the present paper we investigate a contact metric manifold satisfying (C) ( ¯ γ ˙ R ) ( · , γ ˙ ) γ ˙ = 0 for any ¯ -geodesic γ , where ¯ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any ¯ -geodesic γ . Also, we prove a structure theorem for a contact metric manifold with ξ belonging to the k -nullity distribution and satisfying (C) for any ¯ -geodesic γ .

A differential geometric characterization of invariant domains of holomorphy

Gregor Fels (1995)

Annales de l'institut Fourier

Let G = K be a complex reductive group. We give a description both of domains Ω G and plurisubharmonic functions, which are invariant by the compact group, K , acting on G by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space M : = G / K . Such an invariant domain Ω with a smooth boundary is Stein if and only if the corresponding domain Ω M M is geodesically convex and the sectional curvature of its boundary S : = Ω M fulfills the condition K S ( E ) K M ( E ) + k ( E , n ) . The term k ( E , n ) is explicitly computable...

A nonlinear Poisson transform for Einstein metrics on product spaces

Olivier Biquard, Rafe Mazzeo (2011)

Journal of the European Mathematical Society

We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If M is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of M .

A unified approach to compact symmetric spaces of rank one

Adam Korányi, Fulvio Ricci (2010)

Colloquium Mathematicae

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

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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