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 Differentiable Manifold possessing a Finsler Metric. Finsler geometry isRiemannian 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.''See also Finsler Metric, Hodge's Theorem, Riemannian Geometry, Tangent Bundle
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, p. 540-542, 1980.