Related papers: Sasakian structures on CR-manifolds

In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coK\"ahler structures, in the same way as K-contact…

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of…

We give examples of compact symplectic manifolds with disconnected contact type boundary in dimension $4n$ for any $n\geq 1$. The example is given by a subset of the tangent bundle of a compact quotient of the complex hyperbolic space…

We construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson manifolds, not every classical observable on a…

We show that contact reductions can be described in terms of symplectic reductions in the traditional Marsden-Weinstein-Meyer as well as the constant rank picture. The point is that we view contact structures as particular (homogeneous)…

This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal,…

In this paper, a comprehensive study of contact and Sasakian structures on the indicatrix bundle of Finslerian warped product manifolds is reconstructed. In addition, the Kahler structure on the tangent bundle of these manifolds is studied…

In this paper, we concern with the Sasaki analogue of Yau uniformization conjecture in a complete noncompact Sasakian manifold with nonnegative transverse bisectional curvature. As a consequence, we confirm that any $5$-dimensional complete…

In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci…

Motivated by a conjecture in [9] we prove that the K\"ahler cone over a regular complete Sasakian manifold is Ricci-flat and projectively induced if and only if it is flat. We also obtain that, up to $\mathcal D_a$-homothetic…

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a…

We propose a new approach to the existence of constant transversal scalar curvature Sasaki structures drawing on ideas and tools from the CR Yamabe problem, establishing a link between the CR Yamabe invariant, the existence of Sasaki…

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…

A contact twisted cubic structure (M,C,S) is a 5-dimensional manifold M together with a contact distribution C and a bundle S of twisted cubics that is compatible with the conformal symplectic form on C. In Engel's classical work, the Lie…

Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the…

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms,…

We study constructions of contact forms on closed manifolds. A notion of strong symplectic fold structure is defined and we prove that there is a contact form on $M \x X$ provided that $M$ admits such a structure and $X$ is contact. This…

This paper consists of two parts. In the first part, we use symplectic homology to distinguish the contact structures on the Brieskorn manifolds $\Sigma(2l,2,2,2)$, which contact homology cannot distinguish. This answers a question from…

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…

A locally conformally Kahler (LCK) manifold is a complex manifold admitting a Kahler covering M, such that its monodromy acts on this covering by homotheties. A compact LCK manifold is called LCK with potential if M admits an authomorphic…