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...

In the present paper we study lightlike submanifolds of almost paracontact metric manifolds. We define invariant lightlike submanifolds. We study radical transversal lightlike submanifolds of para-Sasakian manifolds and investigate the geometry of distributions. Also we introduce a general notion of paracontact Cauchy-Riemann (CR) lightlike submanifolds and we derive some necessary and sufficie...

We study the Lie algebra of innnitesimal isometries of 7{dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there are no innnites-imal isometry of constant length on a 7{dimensional 3{Sasakian manifold (not isometric to a space form) except the linear comb...

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

The main technical result of the paper is a Bochner type formula for the sub-laplacian on a quaternionic contact manifold. With the help of this formula we establish a version of Lichnerowicz’ theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(n)Sp(1) components of the qc-Ricci curvature. It is shown that in the case of a 3-Sasakian manifold the l...

In the present paper, we have studied curvature properties of Schouten-van Kampen connection on n-dimensional Para Sasakian manifold and obtained some new results. Also, projective tensor, concircular Nijenhuis tensor for Para-Sasakian with respect to connection.

In this paper we study *-Conformal {\eta}-Ricci soliton on Sasakian manifolds. Here, discuss some curvature properties manifold admitting soliton. We obtain significant results in manifolds satisfying R({\xi},X).S = 0, S({\xi},X).R {\overline}P({\xi},X).S where {\overline}P is Pseudo-projective tensor.The conditions for {\Phi}-conharmonically flat and {\Phi}-projectively have been obtained arti...

We begin this review with a brief history of the subject for our exposition shall have little to do with the chronology. In 1960 Sasaki [Sas 1] introduced a geometric structure related to an almost contact structure. This geometry became known as Sasakian geometry and has been studied extensively ever since. In 1970 Kuo [Kuo] refined this notion and introduced manifolds with Sasakian 3-structur...

We obtain results on the vanishing of divergence of Riemannian and Projective curvature tensors with respect to semi-symmetric metric connection on a trans-Sasakian manifold under the condition φ(gradα) = (n− 2)gradβ.