The Studies On Two Kinds Of Non-Rieman-nian Quantities (?)-curvature And H-curvature

In recent research of Finsler geometry, two important non-Riemannian quantities areintroduced, that is,-curvature and (?)-curvature. The study of them may lead to someglobal results. In this paper, we focus on those two significant geometric quantities. Firstly,we investigate-curvature and (?)-curvature in conformal Finsler geometry. Conformalgeometry is a significant subject in Finsler geometry and has been extensively studied. Onthe basis of known results, we get the relation of-curvature, and that of (?)-curvaturefor conformally related Finsler metrics. Secondly, we consider-curvature or(?)-curvature in projective Finsler geometry. It’s an important question to characterize orclassify projectively flat Finsler metrics with special Riemannian or non-Riemanniancurvature properties. Then we classify a class of projectively flat (α,β)-metrics withalmost vanishing-curvature or (?)-curvature. Next, the formula of-curvature for(α,β)-metrics is calculated and a global result is proved. In the end, using the formulaobtained and the relation of-curvature for conformally related Finsler metrics, weclassify a category of conformally flat (α,β)-metrics with almost vanishing(?)-curvature.