On ( α, β ) - metrics with isotropic E-curvature - Boydon, Kai Brynne M. (Institute of Mathematics, College of Science, University of the Philippines Diliman, 2013)
A Finsler manifold, intuitively, is a manifold which is infinitesimally a Banach space. It is a manifold where each tangent space is quipped with a Mikowski norm, a norm which is not induced by an inner product. The E-curvature is an important non-Riemann quantity in Finsler Geometry. It is closely related to the S-curvature S (x,y). The S-curvature, in turn, interacts with the flag curvature. The flag curvature K=K (P,y) is a Riemann quantity which is a natural extension of the sectional curvature in Finsler Geometry. Our focus is a class of computable Finsler metrics ( α, β ) - metrics with E-curvature E = 0. We also study those ( α, β ) - metrics that have almost isotropic S-curvature but not having isotropic E-curvature.