Related papers: Generalized almost contact structures and generali…
In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.
This is an expository paper describing the geometry of certain Sasakian-Einstein manifolds. Such manifolds have recently become of interest due to Maldacena's AdS/CFT conjecture. They describe near-horizon geometries of branes at conical…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
The purpose of this paper is to study the Sasakian geometry on odd dimensional sphere bundles over a smooth projective algebraic variety $N$ with the ultimate, but probably unachievable goal of understanding the existence and non-existence…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…
We show that, for any given $q\geq 0$, any Sasakian structure on a closed manifold $M$ is approximated in the $C^{q}$-norm by structures induced by CR embeddings into weighted Sasakian spheres. In order to obtain this result, we also…
Bourgeois proved in [5] that odd-dimensional tori admit a contact structure. We shall prove a more general result: Any odd-dimensional parallelisable closed manifold admits a contact structure. This implies that a solvmanifold $\Gamma…
Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…
In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.
The study of harmonicity for almost contact metric structures was initiated by Vergara-D\'iaz and Wood and continued by Gonz\'alez-D\'avila and the present author. By using the intrinsic torsion and some restriction on the type of almost…
In this paper, left-invariant almost contact metric structures on three-dimensional non-unimodular Lie groups are investigated. It is proved that for every Riemannian Lie group, there is one of these structures. In addition, left-invariant…
There are introduced and studied a pair of associated Schouten-van Kampen affine connections adapted to the contact distribution and an almost contact B-metric structure generated by the pair of associated B-metrics and their Levi-Civita…
For a finite family of 3-dimensional almost contact metric manifolds with closed the structure form $\eta$ is described a construction of an almost contact metric manifold, where the members of the family are building blocks - cells.…
The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in…
3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. This paper throws new light on their geometric structure which reveals to be…
We consider Courant and Courant-Jacobi brackets on the stable tangent bundle $TM\times\mathds{R}^h$ of a differentiable manifold and corresponding Dirac, Dirac-Jacobi and generalized complex structures. We prove that Dirac and Dirac-Jacobi…
A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures…
In this short note we present some remarks concerning anti-quasi-Sasakian manifolds. Some proofs of their basic properties are simplified. We also discuss some canonical invariant distributions which exist on every anti-quasi-Sasakian…
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a…