arXiv research

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

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

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

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…

No complete Einstein hypersurfaces found in a specific type of Sasakian manifold.

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

Einstein like $(\varepsilon)$-para Sasakian manifolds are introduced. For an $(\varepsilon)$-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like $(\varepsilon)$-para Sasakian manifold is obtained and it…

The study lifts certain Sasakian manifolds to quasi-Einstein spacetimes.

The paper provides formulae for CR invariants in Sasakian η-Einstein manifolds.

Constructs solutions to Einstein-Maxwell-current system using Sasakian manifolds.

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.

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…

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…

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…

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…

Complete gradient Einstein-type Sasakian manifolds with α=0 are trivial or isometric to the unit sphere.

The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on $\scriptstyle{S^2\times S^3}$ and on $\scriptstyle{(S^2\times S^3)# (S^…

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit…

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

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.

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-…

Approximates compact and non-compact Sasakian manifolds in spheres.

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

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

We show that #8(S^2 times S^3) admits two 8-dimensional complex families of inequivalent non-regular Sasakian-Einstein structures. These are the first known non-regular Sasakian-Einstein metrics on this 5-manifold.

We show that $\scriptstyle{#9(S^2\times S^3)}$ admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound $\scriptstyle{b_2(M)\leq8}$ which holds for any regular Sasakian-Einstein $\scriptstyle{…

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…

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…

Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions greater than 1. These have extremal Sasaki metrics with constant scalar curvature. Moreover, we present further examples of both Sasaki…

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…

Let $S$ be a compact Sasakian manifold which does not admit non-trivial Hamiltonian holomorphic vector fields. If there exists an Einstein-Sasakian metric on $S$, then it is unique.

The theory of ambient spaces is useful to define CR invariant objects, such as CR invariant powers of the sub-Laplacian, the $P$-prime operators, and $Q$-prime curvature. However in general, it is difficult to write down these objects in terms of the Tanaka-Webster connection. In this paper, we give those explicit form…

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…

Study on para-Sasakian metrics and their solitons.

We prove that any non-Sasakian contact metric (κ,μ)-space admits a canonical η-Einstein Sasakian or η-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find the values of κand μfor which such metrics are Sasaki-Einstein and paraSasaki-Einstein. Convers…

Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.

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 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 …

In a recent article the first three authors proved that in dimension $4m+1$ all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also conjectured that all such homotopy spheres in dimension $4m-1, m\geq2$ admit Sasakian-…

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian …

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.

Introduces pqc structures, generalizing para 3-Sasakian geometry.

We show that a Sasakian metric which also satisfies the gradient Ricci soliton equation is necessarily Einstein.

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

This paper studies Sasakian quasi-Killing spinors on 3D Sasakian manifolds.

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

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

The paper proves the existence of Sasaki-Einstein metrics on specific Sasakian manifolds.