In the present paper, we shall prove new characterizations of Berwald spaces and Landsberg spaces. The main idea inthis research is the use of the so-called average Riemannian metric.

A mean-field density functional theory is developed to describe the and curvature dependent isotropic-to-nematic transition of elongated bendable proteins.

We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...

In this paper, we have considered surfaces with constant negative Gaussian curvature in the simply isotropic 3-Space by defined Sauer and Strubeckerr. Firstly, studied II-flat, minimal II-minimal, second curvature, mean of (SCNC) 3-space. Surfaces symmetry are obtained when curvatures equal. Further, investigated Casorati, tangential amalgamatic SCNC.

In the present paper, we find out necessary and sufficient conditions for a Finsler surface $(M,F)$ to be Landsbregian in terms of Berwald curvature $2$-forms. We study surfaces which satisfy some flag $K$ conditions, viz., $V(K)=0,\,\,V(K)= -\mathcal{I}/F^2$ $V(K)=-\mathcal{I}\,K,$ where $\mathcal{I}$ is Cartan scalar. order do so, investigate geometric objects associated with global distribut...

In this paper, we study the well-known unicorn problem for Finsler metrics. First, prove that every homogeneous Landsberg surface has isotropic flag curvature. Then by using particular form of curvature, a rigidity result on surfaces. Indeed, is Riemannian or locally Minkowskian. Thus, give an affirmative answer to Xu-Deng's conjecture in two-dimensional manifolds.

There are two definitions of Einstein-Finsler spaces introduced by Akbar-Zadeh, which we will show is equal along the integral curves $I$-invariant projective vector fields. The sub-algebra $C$-projective fields, leaving $H$-curvature invariant, has been studied extensively. Here on a closed Finsler space with negative definite Ricci curvature reduces to that Killing Moreover, if an admits such...