arXiv research

The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.

Study immersions of Sasakian manifolds into Sasakian space forms.

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

The object of this paper is to study the invariant submanifolds of Sasakian generalized-Sasakian-space-form. Here, we obtain some equivalent conditions for an invariant submanifold of a Sasakian generalized-Sasakian-space-forms to be totally geodesic.

We show that the contact reduction can be specialized to Sasakian manifolds. We link this Sasakian reduction to Kähler reduction by considering the Kähler cone over a Sasakian manifold. We present examples of Sasakian manifolds obtained by $S^1$ reduction of standard Sasakian spheres.

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

Defines generalized Sasakian structures in contact geometry.

Study on lightlike geometry in indefinite Sasakian statistical manifolds.

Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.

Sasakian immersions prove Sasaki-Ricci solitons are η-Einstein with rational constants.

We find a family of five dimensional completely solvable compact manifolds that constitute the first examples of $K$-contact manifolds which satisfy the Hard Lefschetz Theorem and have a model of Tievsky type just as Sasakian manifolds but do not admit any Sasakian structure.

Uniformizes compact Sasakian manifolds into circle bundles.

The purpose of this paper is to study *-Ricci tensor on Sasakian manifold. Here, φ-confomally flat and confomally flat *-η-Einstein Sasakian manifold are studied. Next, we consider *-Ricci symmetric conditon on Sasakian manifold. Finally, we study a special type of metric called *-Ricci soliton on Sasakian manifold.

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

We find some curvature properties of 3-quasi-Sasakian manifolds which are similar to some well-known identities holding in the Sasakian case. As an application, we prove that any 3-quasi-Sasakian manifold of constant horizontal sectional curvature is necessarily either 3-α-Sasakian or 3-cosymplectic.

The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and $η$-Einstein cases when the codimension of the immersion is $4$. Moreover, we exhib…

Survey of recent progress in Sasakian geometry.

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

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

The aim of this paper is to study Sasakian immersions of (non-compact) complete regular Sasakian manifolds into the Heisenberg group and into $\mathbb{B}^N\times \mathbb{R}$ equipped with their standard Sasakian structures. We obtain a complete classification of such manifolds in the $η$-Einstein case.

We show certain symmetry of the dimensions of cohomologies of the funda- mental groups of compact Sasakian manifolds by using the Hodge theory of twisted basic cohomology. As applications, we show that the polycyclic fundamental groups of compact Sasakian manifolds are virtually nilpotent and Sasakian solvmanifolds are…

We show that the Malcev Lie algebra of the fundamental group of a compact $2n+1$-dimensional Sasakian manifold with $n\ge 2$ admits a quadratic presentation by using Morgan's bigradings of minimal models of mixed-Hodge diagrams. By using bigradings of minimal models, we also simplify the proof of the result of Cappelle…

Simplified proofs and new distributions on anti-quasi-Sasakian manifolds.

Nilpotent Sasakian manifolds are Heisenberg nilmanifolds.

Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifol…

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…

In this paper we provide a second variation formula for L-minimal Lagrangian submanifolds in a pseudo-Sasakian manifold. We apply it to the case of Lorentzian-Sasakian manifolds and relate the L-stability of L-minimal Legendrians in a Sasakian M to their L-stability in an associated Lorentzian-Sasakian structure on M.

Researchers provide explicit parametrizations for Sasakian space forms.

In this paper we study the 3-dimensional $(\varepsilon)$-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon )$-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric $(\varepsilon)$-para Sasakian 3 -manifold is an indefinite space form…

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

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…

Complex structures found on product of Sasakian manifolds.

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

We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension greater than five.

Study Higgs bundles and flat connections on quasi-regular Sasakian manifolds.

We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…

Study on LP-Sasakian manifolds with generalized η-Ricci solitons.

Local Sasaki-Ricci solitons are $η$-Einstein in certain fiber products of homogeneous Sasakian manifolds.

We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using th…

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

We complete the reduction of Sasakian manifolds with the non-zero case by showing that Willett's contact reduced space is compatible with the Sasakian structure. We then prove the compatibility of the non-zero Sasakian (in particular, contact) reduction with the reduction of the Kähler (in particular, symplectic) cone.…

Approximates compact and non-compact Sasakian manifolds in spheres.

Defines a new Poisson structure for generalized Sasakian spaces.

Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-component of the basic Euler class characterizes the existence of compatible Sasakian metrics for given small deformations of the Reeb flow as tra…

Study biharmonic hypersurfaces in Sasakian space form using Tanaka-Webster connection.

We show that on a Sasakian 3-sphere the Sasaki-Ricci flow initiating from a Sasakian metric of positive transverse scalar curvature converges to a gradient Sasaki- Ricci soliton. We also show the existence and uniqueness of gradient Sasaki-Ricci soliton on each Sasakian 3-sphere.

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…