We give some examples of slant submanifolds of cosymplectic manifolds. Also, we study some special slant submanifolds, called austere submanifolds, and establish a relation between minimal and anti-invariant submanifolds which is based on properties of the second fundamental form. Moreover, we give an example to illustrate our result.
We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.
The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian -Sasakian manifold. We study some curvature properties of an Lorentzian -Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally -symmetric, -symmetric, locally projective -symmetric, -projectively flat Lorentzian -Sasakian manifold with respect to the quarter-symmetric metric connection.
In this paper, we characterize a class of biharmonic maps from and between product manifolds in terms of the warping function. Examples are constructed when one of the factors is either Euclidean space or sphere.
The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian -Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian -Sasakian manifold with respect to quarter-symmetric metric connection.
The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a -almost Kenmotsu manifold satisfying the curvature condition is locally isometric to the hyperbolic space . Also in -almost Kenmotsu manifolds the following conditions: (1) local symmetry , (2) semisymmetry , (3) , (4) , (5) locally isometric to the hyperbolic space are equivalent. Further, it is proved that a -almost Kenmotsu manifold satisfying...