Almost Hermitian structures on the frame bundle of an almost Hermitian manifold
Almost Hermitian surfaces with vanishing Tricerri-Vanhecke Bochner curvature tensor
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 -structure
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...
Almost Kenmotsu -manifolds.
Almost Para-contact Finsler Connections on Vector Bundle
Almost para-contact Finsler connections on vector bundle.
Almost product Riemannian manifolds
Almost product structures and Poisson reduction of presymplectic systems.
Almost pseudo symmetric Sasakian manifold admitting a type of quarter symmetric metric connection
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.
Almost -contact structures
Almost-Einstein manifolds with nonnegative isotropic curvature
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 anti-Kählerian Einstein structure on the tangent bundle of a space form
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 twistor theory to the non-hyperbolicity of certain compact symplectic Kähler manifolds.
An example of a 6-dimensional flat almost Hermitian manifold
An improved Chen-Ricci inequality for special slant submanifolds in Kenmotsu space forms
B. Y. Chen [Arch. Math. (Basel) 74 (2000), 154-160] proved a geometrical inequality for Lagrangian submanifolds in complex space forms in terms of the Ricci curvature and the squared mean curvature. Recently, this Chen-Ricci inequality was improved in [Int. Electron. J. Geom. 2 (2009), 39-45]. On the other hand, K. Arslan et al. [Int. J. Math. Math. Sci. 29 (2002), 719-726] established a Chen-Ricci inequality for submanifolds, in particular in contact slant submanifolds, in Kenmotsu...
An introduction to symplectic topology
An Obstruction to the Existence of Affine Structures.
An Osserman-type condition on g.f.f-manifolds with Lorentz metric
A condition of Osserman type, called the φ-null Osserman condition, is introduced and studied in the context of Lorentz globally framed f-manifolds. An explicit example shows the naturality of this condition in the setting of Lorentz 𝓢-manifolds. We prove that a Lorentz 𝓢-manifold with constant φ-sectional curvature is φ-null Osserman, extending a well-known result in the case of Lorentz Sasaki space forms. Then we state a characterization of a particular class of φ-null Osserman 𝓢-manifolds....
Anosov flows and non-Stein symplectic manifolds
We simplify and generalize McDuff’s construction of symplectic 4-manifolds with disconnected boundary of contact type in terms of the linking pairing defined on the dual of 3-dimensional Lie algebras. This leads us to an observation that an Anosov flow gives rise to a bi-contact structure, i.e. a transverse pair of contact structures with different orientations, and the construction turns out to work for 3-manifolds which admit Anosov flows with smooth invariant volume. Finally, new examples of...
Anti-invariant Riemannian submersions from almost Hermitian manifolds
We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold...