芬斯勒流形

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芬斯勒流形是一个在每个切空间有巴拿赫(Banach)範數的微分流形，该巴拿赫范数是位置的光滑函数并满足以下条件：

对M中的每点x，对切空间TxM中的每一向量v，如下函数的二阶导数

在v是正定的。

黎曼流形(但不包括伪黎曼流形)是芬斯勒流形的特例。

可微曲线γ的长度由下式给出

注意这是一个重参数化不变量，测地线是长度在变分时取极值的曲线。


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