Journal of Finsler Geometry and its Applications
Volume:2 Issue: 2, Nov 2021

In this paper‎, ‎we study and investigate the conformal change of projective Ricci curvature of Kropina metrics‎. ‎Let F and  F˜ be two conformally related Kropina metrics on a manifold M‎. ‎We prove that PRic˜=  PRic if and only if the conformal transformation is a homothety‎.

In this paper relation between pseudoconvex and quasi convex functions is introduced in the context of Riemannian manifolds. In this setting first order characterization of pseudoconvex (strongly pseudoconvex) functions is obtained.

Let (M,F) be a Finsler manifold and G be the Sasaki-Finsler metric on TM∼. In this paper, we investigate some properties of Sasaki-Finsler metric which is pure with respect to some paracomplex structures on TM∼. Also, we show that the curvature tensor field of the Levi-Civita connection on (TM,G) is recurrent or pseudo symmetric if and only if (M,F) is locally Eulidean or locally Minkowski space.

In this paper, we find a new non-Riemannian quantity for (α, β)-metrics that is closely related to the S-curvature. We call it the S˜-curvature. Then, we show that an (α, β)-metric is Riemannian if and only if S˜=0. For a Randers metric, we find the relation between S-curvature and S∼-curvature.

The use of a distribution ‎‎D‎ ‎allows the presence of geometric structures such as almost product ‎structure‎‎,‎‎‎ so that the equivalent of these structures can be seen in ‎tangent ‎super‎manifolds. We define associated ‎adapted ‎linear‎ superconnections‎‎ ‎‎and find all ‎‎linear ‎super‎‎connections‎‎ on the ‎supermanifold ‎‎M ‎adapted to ‎‎D.

In this paper we study the Riemannian geometry of simple Lie groups SO(3,R), SL(2,R) and SO(1,3), equipped with a left invariant Riemannian metric. We consider left invariant Randers metrics induced by these left invariant Riemannian metrics. Then, in each case, we obtain the S-curvature and show that although these Randers metrics are not of Berwald or Douglas type but in the case of SO(3,R) it is of almost isotropic S-curvature. Finally, we give the S-curvature of left invariant Randers metrics on four-dimensional Einstein Lie groups.

In this paper, we introduce a class of Finsler metrics with interesting curvature properties. Then we find necessary and sufficient condition under which these Finsler metrics are locally dually flat and Douglas metrics.

Let F = √α(α + β) be a conformally flat square-root (α; β)-metric on a manifold M of dimension n ≥ 3, where α = √aij(x)yiyj is a Riemannian metric and β = bi(x)yi is a 1-form on M. Suppose that F has relatively isotropic mean Landsberg curvature. We show that F reduces to a Riemannianmetric or a locally Minkowski metric.

Let (Mn,g) be a Riemannian manifold and TM its tangent bundle. In this paper, we determine the infinitesimal fiber-preserving paraholomorphically projective (IFPHP) transformations on TMwith respect to the Levi-Civita connection the deformed complete lift metric G=gC+(fg)V, where f is a nonzero differentiable function on Mn and gC and gV are the complete lift and the vertical lift of g on TM, respectively. Also, the infinitesimal complete lift, horizontal lift and vertical lift paraholomorphically projective transformations on (TM,Gf) are studied.

In this paper, we study conformal vector fields on Finsler manifolds. Let (M,g) be an Einstein-Finsler manifold of dimension n ≥ 2. Suppose that V is conformal vector field on M. We show that V is a concircular vector field.

Current paper deals with the property of dually flatness of Finsler spaces with some special (α,β )-metrics constructed via Randers-β change. Here, we find necessary and sufficient conditions under which these (α,β )-metrics are locally dually flat. Finally, we conclude the relationship between locally dully flatness of these Randers-β change of Finsler metrics.

In this paper, we study the conformal vector fields of Finsler space with the special metric, known as Z. Shen's Square metric. Further we defined the special metric in Riemannian metric α  and 1-form β and its norm. Then we characterize the PDE's of conformal vector fields on special metric.