arXiv research

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

Study of 3D trans-Sasakian manifolds using Newman--Penrose formalism.

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

Hyperbolic solitons on trans-Sasakian space forms and their submanifolds

Study on astheno-Kähler structures on product manifolds.

Study on Ricci solitons and related metrics in 3D trans-Sasakian manifolds.

Study on 3D trans-Sasakian manifolds with η-Einstein solitons.

The object of the present paper is to study some properties of 3-dimensional trans-Sasakian manifold whose metric is η-Yamabe soliton. We have studied here some certain curvature conditions of 3-dimensional trans-Sasakian manifold admitting η-Yamabe soliton. Lastly we construct a 3-dimensional trans-Sasakian manifold s…

The article defines and analyzes Clairaut anti-invariant maps between Riemannian and trans-Sasakian manifolds.

Tachibana operator applied to invariant submanifolds of Lorentzian trans-Sasakian manifolds.

This paper is devoted to the study of curvature and torsion of almost contact curves in trans-Sasakian 3-Manifolds. The conditions for the frenet curves to be almost contact curves in trans-Sasakian 3-manifolds have been obtained.

The study examines curvature tensors and solitons in Lorentzian trans-Sasakian space forms.

In this paper, we obtain some sufficient conditions for a 3-dimensional compact trans-Sasakian manifold of type $(α,β)$ to be homothetic to a Sasakian manifold. A characterization of a 3-dimensional cosymplectic manifold is also obtained.

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product cont…

Paper applies Newman-Penrose formalism to ACM manifolds.

Generalized (κ,μ)-space forms are introduced and studied. We examine in depth the contact metric case and present examples for all possible dimensions. We also analyse the trans-Sasakian case.

In this paper, we study warped product submanifolds of nearly trans-Sasakian manifolds. The non-existence of the warped product semi-slant submanifolds of the type $N_θ\times{_{f}N_T}$ is shown, whereas some characterization and new geometric obstructions are obtained for the warped products of the type $N_T\times{_{f}…

An almost contact metric structure is parametrized by a section of an associated homogeneous fibre bundle, and conditions for this to be a harmonic section, and a harmonic map, are studied. These involve the characteristic vector field, and the almost complex structure in the contact subbundle. Several examples are giv…

In this paper, we introduce the trans-para-Sasakian manifolds and we study their geometry. These manifolds are an analogue of the trans-Sasakian manifolds in the Riemannian geometry. We shall investigate many curvature properties of these manifolds and we shall give many conditions under which the manifolds are either …

We give a notion of compatibility between a Riemannian structure and a Jacobi structure. We prove that in case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, …

We give a notion of compatibility between a Riemannian metric and a Jacobi structure. We prove that in case of Poisson structures, contact structures and locally conformally symplectic structures, fundamental examples of Jacobi structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, $\fr…

In this paper, we introduce the notion of Koszul-Vinberg-Nijenhuis structures on a left-symmetric algebroid as analogues of Poisson-Nijenhuis structures on a Lie algebroid, and show that a Koszul-Vinberg-Nijenhuis structure gives rise to a hierarchy of Koszul-Vinberg structures. We introduce the notions of ${\rm KVΩ}$-…

Defines structure constants for specific geometric structures on Lie groups.

Study on $G_2^*$ structures and almost para-contact structures in 7D.

Defines a new Poisson structure for generalized Sasakian spaces.

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic structures, we get respectively Rie…

Study on types of generalized hypercomplex structures on tori and Kodaira-Thurston surface.

Classifies complex Dirac structures with invariants and local structure.

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

3D projective structures can be metrized with conformal structures.

Hypersymplectic structures with torsion on Lie algebroids are investigated. We show that each hypersymplectic structure with torsion on a Lie algebroid determines three Nijenhuis morphisms. From a contravariant point of view, these structures are twisted Poisson structures. We prove the existence of a one-to-one corres…

Study equivalence between Hessian and Born structures on tangent bundles.

Introduces compatibility between Dirac structures and Nijenhuis tensors.

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…

Introduces semi-abelian generalized complex structures.

Introduces VB-structures for geometric objects on manifolds.

The paper studies nilpotent structures in oriented neutral vector bundles and neutral hyperKähler structures.

Spin-structures on real Bott manifolds with Kähler structure are characterized.

Expanding on previous work, this note generalizes geometric structures results.

Exotic hypercomplex structures on a torus are proven to not exist.

Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying structure is conformally symplectic, then one obtains a PCS-structure. In the current ar…

In this paper, we show the existence of (co-oriented) contact structures on certain classes of $G_2$-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure (and so any manifold with $G_2$-structure) admits an almost contact structure. We…

Two Kähler structures are PCR equivalent in the Siegel domain.

We characterize the Dirac structures that are parallel with respect to Gualtieri's canonical connection of a generalized Riemannian metric. On the other hand, we discuss Dirac structures that are images of generalized tangent structures. These structures turn out to be Dirac structures that, if seen as Lie algebroids, …

Introduces holed cone structures to generalize cone structures on 3-manifolds.

The study classifies complex symplectic structures on 4D Lie algebras and constructs hypersymplectic structures.

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 …

We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact structures from a counterpart of generalized complex structures on odd-dimensiona…