Narrow Results

Here, it is shown that if a forward geodesically complete Finsler manifold admits a circle preserving change of metric then its indicatrix is conformally diffeomorphic to the Euclidean sphere S^n-1. Moreover, if the Finsler manifold is absolutely homogeneous and of scalar flag curvature then it is a Riemannian manifold of constant sectional curvature. These results provide a geometric interpretation for existence of solutions to the certain ODE on the Riemannian tangent space.

Conformal, concircular, quasi-conformal and conharmonic curvature tensors play an important role in Riemannian geometry. In this paper, we study on normal complex contact metric manifolds under flatness conditions of these tensors.