Finsler manifold

In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x, −) is provided on each tangent space TxM, that enables one to define the length of any smooth curve γ : [a, b] → M as L ( γ ) = ∫ a b F ( γ ( t ) , γ ˙ ( t ) ) d t . {\displaystyle L(\gamma )=\int _{a}^{b}F\left(\gamma (t),{\dot {\gamma }}(t)\right)\,\mathrm {d} t.} Finsler manifolds are more general than Riemannian manifolds since the tangent norms need not be induced by inner products.

Source: Wikipedia — Finsler manifold (CC BY-SA 4.0)

Finsler manifold

In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x, −) is provided on each tangent space TxM, that enables one to define the length of any smooth curve γ : [a, b] → M as L ( γ ) = ∫ a b F ( γ ( t ) , γ ˙ ( t ) ) d t . {\displaystyle L(\gamma )=\int _{a}^{b}F\left(\gamma (t),{\dot {\gamma }}(t)\right)\,\mathrm {d} t.} Finsler manifolds are more general than Riemannian manifolds since the tangent norms need not be induced by inner products.

Source: Wikipedia "Finsler manifold" · CC BY-SA 4.0

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