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Almost Hermitian surfaces with vanishing Tricerri-Vanhecke Bochner curvature tensor

Y. Euh, J. Lee, J. H. Park, K. Sekigawa, A. Yamada (2011)

Colloquium Mathematicae

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.

Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact 3 -structure

Francisco Martín Cabrera (1998)

Czechoslovak Mathematical Journal

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...

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 example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono, Yuji Sano, Naoto Yotsutani (2012)

Annales de l’institut Fourier

Donaldson proved that if a polarized manifold ( V , L ) has constant scalar curvature Kähler metrics in c 1 ( L ) and its automorphism group Aut ( V , L ) is discrete, ( V , L ) is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where Aut ( V , L ) is not discrete.

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