Randers space and a Finsler space

Question

What is the difference between Randers spaces and Finsler spaces?

Answer 1

1. A Randers manifold is a special case of a non-reversible Finsler manifold $(M,F)$, where the Finsler function $$F(x,v)~=~\sqrt{g_{ij}(x)v^iv^j}+b_i(x)v^i, \qquad (g^{-1})^{ij}b_ib_j~<~1,$$ is a sum of a square root term and linear term.

2. a Riemannian manifold $(M,g)$ is a Randers manifold with $b_i\equiv 0$.