Finsler Space
A general space based on the line element
with 
for 
a function on the tangent bundle 
, and homogeneous of degree 1 in 
. Formally, a Finsler space is a smooth manifold possessing a Finsler metric. Finsler geometry is Riemannian geometry without the restriction that the line element be quadratic and of the form
A compact boundaryless Finsler space is locally Minkowskian iff it has 0 "flag curvature."
REFERENCES:
Akbar-Zadeh, H. "Sur les espaces de Finsler à courbures sectionnelles constantes." Acad. Roy. Belg. Bull. Cl. Sci. 74, 281-322, 1988.
Bao, D.; Chern, S.-S.; and Shen, Z. (Eds.). Finsler Geometry. Providence, RI: Amer. Math. Soc., 1996.
Chern, S.-S. "Finsler Geometry is Just Riemannian Geometry without the Quadratic Restriction." Not. Amer. Math. Soc. 43, 959-963, 1996.
Iyanaga, S. and Kawada, Y. (Eds.). "Finsler Spaces." §161 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 540-542, 1980.
