On a compact oriented Finsler manifold without boundary, every cohomology class has a unique
harmonic representation. The dimension of the space
of all harmonic forms of degree 
is the 
th Betti number of the manifold.
Hodge's Theorem
See also
Betti Number, Cohomology, Dimension, Finsler SpaceExplore with Wolfram|Alpha
References
Chern, S.-S. "Finsler Geometry is Just Riemannian Geometry without the Quadratic Restriction." Not. Amer. Math. Soc. 43, 959-963, 1996.Referenced on Wolfram|Alpha
Hodge's TheoremCite this as:
Weisstein, Eric W. "Hodge's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HodgesTheorem.html