arXiv research

Defines generalized Sasakian structures in contact geometry.

Defines a new Poisson structure for generalized Sasakian spaces.

We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact structures. We obtain a generalized Sasakian structure on a non-compact manifold which…

Spinorially constructs Sasakian and 3-Sasakian structures in arbitrary dimensions.

New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.

Study classifies quasi-Sasakian 3-manifolds, linking them to Sasakian and co-Kähler structures.

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of Sasakian-Einstein metrics on manifolds homeomorphic to $S^2\times S^5.$ Then we use a gen…

The paper studies a new structure on contact manifolds and its foliation properties.

The present paper is devoted to quasi-Para-Sasakian manifolds. Basic properties of such manifolds are obtained and general curvature identities are investigated. Next it is proved that if $M$ is quasi-Para-Sasakian manifold of constant curvature $K$. Then $K$ $\leq 0$ and $(i)~$if $K=0$, the manifold is paracosymplecti…

Extends corner structure study to general case, constructs normal Trans-Sasakian structures.

The Hessian geometry is the real analogue of the Kähler one. Sasakian geometry is an odd-dimensional counterpart of the Kähler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous to the one between Hessian and Kähler manifolds. In particular, we construct a Sasaki…

We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group $H_{2n + 1}$. Furthermore, we classify Sasakian Lie algebras of dimension 5 and determine which of th…

Introduces pqc structures, generalizing para 3-Sasakian geometry.

The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

Researchers provide explicit parametrizations for Sasakian space forms.

The paper constructs Sasakian lifts from Kähler manifolds and studies their properties.

Complex structures found on product of Sasakian manifolds.

This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal, almost) contact and generalized Sasakian structures. A few of these properties are n…

We provide a general method to construct examples of quasi-Sasakian 3-structures on a (4n+3)-dimensional manifold. Moreover, among this class, we give the first explicit example of a compact 3-quasi-Sasakian manifold which is not the global product of a 3-Sasakian manifold and a hyper-Kähler manifold.

The study examines extensions of Lie algebras with specific geometric structures.

Study on negative Sasakian structures on specific 5-manifolds.

We carry on a systematic study of nearly Sasakian manifolds. We prove that any nearly Sasakian manifold admits two types of integrable distributions with totally geodesic leaves which are, respectively, Sasakian or $5$-dimensional nearly Sasakian manifolds. As a consequence, any nearly Sasakian manifold is a contact ma…

Study explores weak generalized K-contact structures in contact metric spaces.

In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …

Extends Sasakian structures to arbitrary contact manifolds.

Clarifies construction of K-contact non-Sasakian Smale-Barden manifolds.

Geometric flows study nearly parallel G2-structures on 3-Sasakian 7-manifolds.

Study $η$-Einstein Sasakian structures on Lie algebras, dividing cases based on center dimension.

Study shows compact Sasakian manifolds are locally Heisenberg up to deformation.

First example of a 5D manifold with K-contact but no Sasakian structure.

A structure on an almost contact metric manifold is defined as a generalization of well-known cases: Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic. Then we consider a semi-invariant $ξ^{\bot}$-submanifold of a manifold endowed with such a structure and two topics are studied: the integrability of distributions de…

Any Sasakian structure can be closely mimicked by embeddings into weighted spheres.

In this paper, we prove an existence theorem of a local moduli space for geometric structures in a very general setting. Then to show the interest of this result, we apply it to the case of sasakian and Sasaki-Einstein structures.

Study on harmonicity of complex structure on product of trans-Sasakian manifolds.

Study on a specific type of Lie algebras with Kähler and contact properties.

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 generally richer compared to the 3-Sasakian subclass. In fact, it turns out that t…

Recent renewed interest in Sasakian manifolds is due mainly to the fact that they can provide examples of generalized Einstein manifolds, manifolds which are of great interest in mathematical models of various aspects of physical phenomena. Sasakian manifolds are odd dimensional counterparts of Kählerian manifolds to w…

The question of whether a Sasakian metric can admit an additional compatible (K-)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some ext…

New constructions of Sasakian and K-contact structures on Smale-Barden manifolds.

Kollár has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In particular, we find the first example of a closed 5-manifold M with $H_1(M,Z)=0$ which …

Study shows lightlike hypersurfaces in indefinite Sasakian manifolds are not symmetric.

Study of instantons on Stiefel manifold with $G_2$ and Sasakian structures.

In this article, we introduce some metallic structures on the tangent bundle of a P-Sasakian manifold by complete lift, horizontal lift and vertical lift of a P-Sasakian structure $(φ, η,ξ)$ on tangent bundle. Then we investigate the integrability and parallelity of these metallic structures.

We prove that a compact nilmanifold admits a Sasakian structure if and only if it is a compact quotient of the generalized Heisenberg group of odd dimension by a co-compact discrete subgroup.

Study 3-Sasakian and G2 structures on manifolds.

Sasakian structures found on tangent sphere bundles of certain symmetric spaces.