arXiv research

Defines generalized Sasakian structures in contact geometry.

Defines a new Poisson structure for generalized Sasakian spaces.

Paper studies invariant submanifolds in Sasakian spaces, finding conditions for total geodesy.

We show that there is no phi-recurrent generalized Sasakian-space-forms, when is a non-zero constant.

The present paper deals with some results of submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-webster connection.

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…

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…

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and obtain many new results including, the necessary and sufficient conditions under whic…

In this paper, we show that a generalized Sasakian space form of dimension greater than three is either of constant sectional curvature; or a canal hypersurface in Euclidean or Minkowski spaces; or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold; or locally a wapred product…

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

The paper establishes new Casorati inequalities for various Riemannian maps and submersions.

We study the general structure of the AdS_5/CFT_4 correspondence in type IIB string theory from the perspective of generalized geometry. We begin by defining a notion of "generalized Sasakian geometry," which consists of a contact structure together with a differential system for three symplectic forms on the four-dime…

Study on curvature properties of N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.

Paper establishes new inequality for Riemannian maps and applies it to various space forms.

The present paper deals with some results of almsot semi-invariant submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.

In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the implications of this theorem with regard to the definition of generalized Sasakian and ge…

We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We consider curves, complex and Lagrangian surfaces and hypersurfaces for the…

The paper derives inequalities for Riemannian submersions and applies them to specific space forms.

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

The paper derives Chen-Ricci inequalities for Riemannian submersions and maps.

In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coKähler structures, in the same way as K-contact structures generalize Sasakian structures. In analogy to the contact case, we dis…

Extends Sasakian structures to arbitrary contact manifolds.

A generalized F-structure is a complex, isotropic subbundle $E$ of $T_cM\oplus T^*_cM$ ($T_cM=TM\otimes_{\mathds{R}}\mathds{C}$ and the metric is defined by pairing) such that $E\cap\bar E^{\perp}=0$. If $E$ is also closed by the Courant bracket, $E$ is a generalized CRF-structure. We show that a generalized F-structur…