Some formulas of Gauss-Bonnet-Chern type in Riemann-Finsler geometry.
In this study, we introduce a new class of function called geodesic semi E-b-vex functions and generalized geodesic semi E-b-vex functions and discuss some of their properties.
We show that a bi-invariant metric on a compact connected Lie group is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric on there is a positive integer such that, within a neighborhood of in the class of left-invariant metrics of at most the same volume, is uniquely determined by the first distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where is simple, can be chosen to be two....