Journal of Finsler Geometry and its Applications
Volume:5 Issue: 2, Dec 2024

Exponential metrics are popular Finsler metrics. Let F be a exponential (α, β)-metric of isotropic S-curvature on manifold M. In this paper,  a Lie sub-algebra of projective vector fields of a Finsler metric F is introduced denoted by SP(F). We classify SP(F) of isotropic S-curvature as a certain Lie sub-algebra of the Kiliing algebra k(M, α).

In this paper we have taken the n-power (α,β)-metric and obtained the condition for projectively flatness and further find the some special cases.

In the generalizing Branciari space, some conclusions from the literature are developed and re-proved in this paper.

In this paper, we study pointwise projectively related Finsler gradient Ricci solitons. We obtain an equation that characterizes the relationship between two pointwise projectively related Finsler gradient Ricci solitons. Further, if two Finsler gradient Ricci solitons (M, F, dVF) and (M, F, dVF) satisfy  some conditions,  we characterize their relationships along the geodesics. In particular, if two Finsler gradient Ricci solitons are both complete, then (M, F, dVF) is expanding or shrinking and (M, F, dVF) is shrinking.

The notion of a weakly symmetric and weakly projective symmetric Riemannian manifolds has been introduced by Tamassy and Binh and then after studied by so many authors such as De, Shaikh and Jana, Shaikh and Hui, Shaikh, Jana and Eyasmin. Recently, Singh and Khan introduced the notion of Special weakly symmetric Riemannian manifolds and denoted such manifold by (SWS)n. A.U. Khan and Q. Khan found some results On Special Weakly Projective Symmetric Manifolds. And P. Verma and S. Kishor found some results on M-Projective Curvature Tensor on (k, µ)- Contact Space Forms. Motivated from the above, we have studied the nature of Ricci tensor R of type (1,1) in a special weakly M-projective symmetric Riemannian manifold (SWMS)n and also explored some interesting results on (SWMS)n.

In this paper, we study some geometric properties of Finsler Σ−spaces with square metric. We prove that Finsler Σ−spaces with square (α, β)−metrics are Riemannian.

In this paper we study invariant Finsler spaces with generalized m-Kropia metrics. We give an explicit formula for the flag curvature of invariant Finsler spaces with generalized m-Kropina metrics on some Lie groups.

In this paper, we study the stability of Sacks-Uhlenbeck α−harmonic maps from a Finsler manifold to a Riemannian manifold and its applications. Then we find conditions under which any non-constant α−harmonic maps from a compact Finsler manifold to a standard unit sphere Sn(n > 2) is unstable.

The aim of the present paper is to study about (ε)-LP-Sasakian mani-folds with generalized symmetric metric connection. We have an example satisfying (ε)-LP-Sasakian manifolds with generalized symmetric metric connection. Further, we studied D-Conformally-flat and ξ-D-Conformally flat curvature conditions in (ε)-LP-Sasakian manifolds with generalized symmetric metric connection.

In this paper, we introduce a statistical generalized recurrent manifold, which its curvature tensorR*, satisfies the generalized recurrent condition ∇*R*=ΓR*+θ H. Next we prove that a statistical generalized recurrent manifold with constant curvature is as same as a generalized recurrent manifold with respect to its Levi-Civita connection. Also we show that a statistical generalized recurrent manifold is neither statistical semi-symmetric, nor statistical Ricci semi-symmetric. Finally we prove that in spite of the Riemannian manifold, a statistical generalized recurrent manifold is not statistical concircular recurrent.

This paper deals with space known as "generalized fifth recurrent Finsler space." The core idea centers around a mathematical object called the" Inheritance Kulkarni-Nomizu product" which is applied to two Ricci tensors satisfy an inheritance property. We apply the inheritance property with Kulkarni - Nomizu product of two Ricci tensosrs by using Lie - derivative in generalized fifth recurrent Finsler space. In addition, we prove that the Lie - derivative of the inheritance Kulkarni - Nomizu product of K-Ricci tensor and H-Ricci tensor vanishes simultaneously.

The (n +1)-dimensional almost metric contact submanifolds wuth maximal CR- submanifolds of (n-1) in the Kenmotsu space forms classified such that n > 5 and h(FX, Y )-h(X, FY )= g(FX,Y)ζ for vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism acting on the tangent space of M, respectively, and ζ a non zero normal vector field to M.