a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...

In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-h-manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space H3(−1) or the Riemannian product H2(−4)× R. c ©2016 All rights reserved.

The paper deals with the study of Z-symmetric manifolds (ZS)n admitting certain cases Schouten tensor (specifically: Ricci-recurrent, cyclic parallel, Codazzi type and covariantly constant), investigate some geometric physical properties manifold. Moreover, we also (ZS)4 spacetimes tensor. Finally, construct an example to verify our result.

Abstract We classify 3-dimensional compact Riemannian manifolds ( M 3 , g ) that admit a non-constant solution to the equation − Δfg +Hess f Ric = μ + λg for some special constants λ ), under assumption manifold has cyclic parallel Ricci tensor. Namely, structures we study here are: positive static triples, critical metrics of volume functional, and total scalar curvature functional. also n -di...

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.