Journal of Finsler Geometry and its Applications
Volume:4 Issue: 1, Jul 2023

In this paper, We characterize a Finsler manifold admitting a conformal transformation such that the difference of the two Ricci tensors is a constant multiple of the metric. Furthermore, we find some results on Finsler manifolds with constant flag curvature admiting a special conformal transformation.

‎The notion of Shen's process was introduced by Tayebi-Najafi in order to construct the Shen connection from the Berwald connection‎. ‎In this paper‎, ‎we study the connection obtained by Shen's L-process on the Chern connection‎. ‎Let (M‎, ‎F) be a Finsler manifold‎. ‎Suppose that D is the linear torsion-free connection obtained by Shen's L-process on Chern's connection‎. ‎First‎, ‎we show the existence and uniqueness of D‎. ‎Then‎, ‎we prove that their hv-curvature coincides if and only if F is a Riemannian ‎metric

In this paper we discuss some results related to angle between geodesic segments in an infinite dimensional and an asymptotic Teichmüller space. Also, we construct a geodesic triangle in Universal Teichmüller space and calculate all of its interior angles.

The BC− recurrent Finsler space introduced by Alaa et al. [1]. Now in this paper, we introduce and extend BC− birecurrent Finsler space by using some properties of different spaces. We study the relationship between Cartan’s second curvature tensor Pijkh and (h)hv torsion tensor Cijk in sense of Berwald. Additionally, the necessary and sufficient condition for some tensors which satisfy birecurrence property will be discuss in different spaces. Four theorems have been established and proved.

In this paper a special class of R-quadratic generalized $(\alpha, \beta)$-metrics are considered. Some properties of this class are investigated. In special case, the Riemann curvature of this metrics is calculated. Moreover, it is proved that, in this class of metrics, there is not any (non-Riemannian) R-quadratic metrics of non-zero scalar curvature.

We establish a local gradient estimate for positive Finsler p-eigenfu-nctions on a complete non-compact Finsler measure space M with its weighted Ricci curvature Ric∞ bounded from below by a non-positive constant. As an application, we obtain the corresponding Harnack inequality.

M. Matsumoto and R. Miron constructed an orthonormal frame for an n-dimensional Finsler space and the frame was called Miron frame .T.N. Pandey and D. K. Diwedi and P. N. Pandey and Manish Gupta studied four- dimensional Finsler spaces in terms of scalars.P. N. Pandey and Manish Gupta also studied four-dimensional Berwald Space with Vanishing h- connection vector ki.Gauree Shankar, G.C.Chaubey and Vinay Pandey studied the main scalar of a Five Dimensional Finsler space.In the present paper, we study a Five dimensional Berwald space with vanishing h connection vectors.

Let F be an (α,β)-metric which is defined by a left invariant vector field and a left invariant Riemannian metric on a simply connected real Lie group G. We consider the automorphism and isometry groups of the Finsler manifold (G,F) and their intersection. We prove that for an arbitrary left invariant vector field X and any compact subgroup K of automorphisms which X is invariant under them, there exists an (α,β)-metric such that K is a subgroup of its isometry group.

The generalized birecurrent Finsler space have been introduced by the Finslerian geometers. The purpose of the present paper is to study three special form of Pijkh in generalized BP􀀀birecurrent space. Weu se the properties of P2-like space, P-space and P-reducible space in the main space to get new spaces that will be called a P2-like generalized BP-recurrent space, P-generalized BP􀀀birecurrent space and P-reducible generalized BP􀀀birecurrent space, respectively. In addition, we prove that the Cartan's firrst curvature tensor Sijkh satisfies the birecurrence property. Certain identities belong to these spaces have been obtained. Further, we end up this paper with some demonstrative examples.

Recent studies show that warped product manifolds are useful in differential geometry as well as in physics. The goal of this paper is to study on some projective invariants of a special product manifold with Finsler metrics arising from warped products. Firstly, we consider the class of weakly Douglas metrics, weaker notion of Douglas metrics, introduced by Atashafrouz, Najafi and Tayebi in [4]. We prove that every Finsler warped product manifold Mn (n ≥ 3) is weakly Douglas if and only if it is Douglas. Finally, under a certian condition, we show that a class of Finsler warped product metric is locally projectively flat if and only if it is of scalar flag curvature.

The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The properties of these special Finsler spaces are studied and the relations between them are singled out.

In this paper, we consider invariant 3-power metric F=(α + β)3</sup>/α2</sup> such that induced by invariant Riemannian metrics a and invariant vector fields X on homogeneous spaces. We give an explicit formula for the flag curvature of invariant 3-power metrics.