Related papers: Sasaki-Einstein and paraSasaki-Einstein metrics fr…

In this note, stimulated by the existence result of Futaki-Ono-Wang for toric Sasaki-Einstein metrics, we obtain new examples of Sasaki-Einstein metrics on S^1-bundles associated to canonical line bundles of P^1-bundles over…

In this paper, we consider the CPE conjecture in the frame-work of $K$-contact and $(\kappa, \mu)$-contact manifolds. First, we prove that if a complete $K$-contact metric satisfies the CPE is Einstein and is isometric to a unit sphere…

We study non-paraSasakian paracontact metric $(\kappa,\mu)$-spaces with $\kappa=-1$ (equivalent to $h^2=0$ but $h\neq0$). These manifolds, which do not have a contact geometry counterpart, will be classified locally in terms of the rank of…

We show that all compact quasi-Einstein metrics of constant scalar curvature in dimension three are locally homogeneous. We accomplish this by using the equivalence of constant scalar curvature quasi-Einstein metrics $(M,g,X)$ and…

The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A $\mathcal{D}$-homothetic transformation is determined as a special gauge transformation. The…

We introduce the notion of $\varepsilon\eta\,$-Einstein $\varepsilon\,$-contact metric three-manifold, which includes as particular cases $\eta\,$-Einstein Riemannian and Lorentzian (para) contact metric three-manifolds, but which in…

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

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n+1)-dimensional Sasakian manifold admits a weakly Einstein metric then its scalar curvature $s$ satisfies $-6\leqslant s…

This paper is a study of three-dimensional paracontact metric (\k{appa},{\mu},{\nu})-manifolds. Three dimensional paracontact metric manifolds whose Reeb vector field {\xi} is harmonic are characterized. We focus on some curvature…

A positive answer is given to the existence of Sasakian structures on the tangent sphere bundle of some Riemannian manifold whose sectional curvature is not constant. Among other results, it is proved that the tangent sphere bundle Tr(G/K),…

We extend Tsuji's iterative construction of complete K\"ahler--Einstein metrics with negative scalar curvature to noncompact K\"ahler manifolds with bounded geometry, using Berndtsson's method from the compact setting. Consequently, given a…

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…

In this paper, we initiate the study of conformal $\eta$-Ricci soliton and almost conformal $\eta$-Ricci soliton within the framework of para-Sasakian manifold. We prove that if para-Sasakian metric admits conformal $\eta$-Ricci soliton,…

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…

Using $S^1$-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn-Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various…

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian…

The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…

We prove an analogue of the Hitchin-Kobayashi correspondence for compact, oriented, taut Riemannian foliated manifolds with transverse Hermitian structure. In particular, our Hitchin-Kobayashi theorem holds on any compact Sasakian manifold.…

In this paper, we define almost paracontact and normal almost paracontact Finsler structures on a vector bundle and find some conditions for integrability of these structures. We define paracontact metric, para- Sasakian and K-paracontact…

In earlier work we have shown that for certain geometric structures on a smooth manifold $M$ of dimension $n$, one obtains an almost para-K\"ahler--Einstein metric on a manifold $A$ of dimension $2n$ associated to the structure on $M$. The…