We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

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 S×S and on (S×S)#(S×S). These give the first known examples of non-regular Sasakian-Einstein 5manifolds. Our method involves describing the Sasakian...

In [4] B. Y. Chen studied warped product CR-submanifolds in Kaehler manifolds. Afterward, I. Hasegawa and I. Mihai [5] obtained a sharp inequality for the squared norm of the second fundamental form for contact CR-warped products in Sasakian space form. Recently Alegre, Blair and Carriago [1] introduced generalized Sasakian space form. The aim of present paper is to study contact CR-warped prod...

Some results on the properties of T -flat, quasiT -flat,  T -flat,  T -flat, T -semi-symmetric,  T Ricci recurrent and T - -recurrent LP-Sasakian manifolds are obtained. It is also proved that an LP-Sasakian manifold satisfying the condition T . 0 S  is an  -Einstein manifold. MSC 2000. 53C15, 53C25, 53C50, 53D15.

We propose a new method to construct degenerate $3$-$(\alpha,\delta)$-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperk\"ahler manifolds. Subsequently, we study homogeneous $3$-$(\alpha, \delta)$-Sasakian and prove that no non-trivial compact examples exist well there is exactly one family nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.

We introduce the notion of even Clifford structures on Riemannian manifolds, which for rank r = 2 and r = 3 reduce to almost Hermitian and quaternion-Hermitian structures respectively. We give the complete classification of manifolds carrying parallel rank r even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler manifolds for r = 2, 3 and 4 respectively...

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.

It is well-known that 7-dimensional 3-Sasakian manifolds carry a oneparametric family of compatible G2-structures and that they do not admit a characteristic connection. In this note, we show that there is nevertheless a distinguished cocalibrated G2-structure in this family whose characteristic connection ∇ c along with its parallel spinor field Ψ0 can be used for a thorough investigation of t...

Riemannian manifolds with positive sectional curvature have been a frequent topic of global Riemannian geometry for over 40 years. Nevertheless, there are relatively few known examples of such manifolds. The purpose of this article is to study the topological properties of some of these examples, the so-called Eschenburg spaces, in detail. In addition to positively curved metrics, some Eschenbu...