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Finsler Space


A general space based on the line element

 ds=F(x^1,...,x^n;dx^1,...,dx^n),

with F(x,y)>0 for y!=0 a function on the tangent bundle T(M), and homogeneous of degree 1 in y. 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

 F^2=g_(ij)(x)dx^idx^j.

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

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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.

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Finsler Space

Cite this as:

Weisstein, Eric W. "Finsler Space." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FinslerSpace.html

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