A new non-Riemannian curvature related to the class of (α, β)-metrics

In this paper, we find a new non-Riemannian quantity for (α, β)-metrics that is closely related to the S-curvature. We call it the S˜-curvature. Then, we show that an (α, β)-metric is Riemannian if and only if S˜=۰. For a Randers metric, we find the relation between S-curvature and S∼-curvature.

Keywords:

Hopf maximum principle , Elliptic operator , (α , β)-metrics , S-curvature