arXiv research

Defines generalized Sasakian structures in contact geometry.

Defines a new Poisson structure for generalized Sasakian spaces.

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…

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…

Survey of recent progress in Sasakian geometry.

Introduces pqc structures, generalizing para 3-Sasakian geometry.

We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi-Yau manifolds are investigated.

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

Study on lightlike geometry in indefinite Sasakian statistical manifolds.

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 show that every Sasakian manifold in dimension $2k+1$ is locally generated by a free real function of $2k$ variables. This function is a Sasakian analogue of the Kähler potential for Kähler geometry. It is also shown that every locally Sasakian-Einstein manifold in $2k+1$ dimensions is generated by a locally Kähler-…

We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are given for the `product' of two Sasakian-Einstein manifolds to be a smooth Sasaki…

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

We review our study of Sasakian geometry as an agent for proving the existence of Einstein metrics on odd dimensional manifolds. Particular emphasis is given to the Sasakian structures occuring on links of isolated hypersurface singularities.

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

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 …

In this note I study the Sasakian geometry associated to the standard CR structure on the Heisenberg group, and prove that the Sasaki cone coincides with the set of extremal Sasakian structures. Moreover, the scalar curvature of these extremal metrics is constant if and only if the metric has $Φ$-sectional curvature $-…

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

3-quasi-Sasakian manifolds were recently studied by the authors as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper some geometric properties of this class of almost 3-contact metric manifolds are briefly reviewed, with an emphasis on those more related to physical applications.

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

In this paper we obtain theorems of Barth-Lefschetz type in Sasakian geometry. As corollaries, this implis connectedness principle and Frankel's type theorem.

In the present paper first, we define the conformal Sasakian manifolds and then we study geometry of invariant, anti-invariant and CR-submanifolds of conformal Sasakian manifolds.

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…

The study introduces a new soliton concept to classify Sasakian 3-manifolds.

Study calibrated geometry in hyperkähler cones and their related spaces.

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 singularities.

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…

Bi-slant submersion generalizes slant and semi-slant submersion.

This is a mainly expository article honoring my recently deceased friend and collaborator Krzysztof Galicki who died after a tragic hiking accident. I give a review of our recent work in Sasakian geometry. A few new results are also presented.

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein structures on many different compact manifolds, including exotic spheres. We also relate…

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres $\script…

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type i…

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…

The purpose of this paper is to study the harmonicity of maps to or from para-Sasakian manifolds. We derive the condition for the tension field of paraholomorphic map between almost para-Hermitian manifold and para-Sasakian manifold. The necessary and sufficient condition for a paraholomorphic map between para-Sasakian…

In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly parallel G2 structure, and nea…

New method constructs degenerate Sasakian manifolds from hyperkähler bundles.

Machine learning predicts topological properties of Calabi-Yau manifolds.

We extend a result of Patodi for closed Riemannian manifolds to the context of closed contact manifolds by showing the condition that a manifold is an $η$-Einstein Sasakian manifold is spectrally determined. We also prove that the condition that a Sasakian space form has constant $φ$-sectional curvature $c$ is spectral…

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are Kähler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit …

The paper studies Clairaut maps on Sasakian manifolds.

We solve the problem posed by Boyer and Galicki about the existence of K-contact simply connected manifolds with no Sasakian structure. Although the result lies in the framework of metric contact geometry, our methods come from contact and symplectic geometry and are based on the method of fat bundles developed by Ster…

On simply connected five manifolds Sasakian-Einstein metrics coincide with Riemannian metrics admitting real Killing spinors which are of great interest as models of near horizon geometry for three-brane solutions in superstring theory [KW]. We expand on the recent work of Demailly and Kollár [DK] and Johnson and Kollá…

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…

We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of $η$-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising them in terms of generalised Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a …

We classify all proper-biharmonic Legendre curves in a Sasakian space form and point out some of their geometric properties. Then we provide a method for constructing anti-invariant proper-biharmonic submanifolds in Sasakian space forms. Finally, using the Boothby-Wang fibration, we determine all proper-biharmonic Hopf…

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

We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler …

The paper examines timelike conformal fields on 3-manifolds and finds they are rigidly tied to specific geometric structures.