In 1939 Weyl showed that the volume of spherical tubes around compact submanifolds M of Euclidean space depends solely on the induced Riemannian metric on M. Can this intrinsic nature of the tube volume be preserved for tubes with more general cross sections \(\mathbb {D}\) than the round ball? Under sufficiently strong symmetry conditions on \(\mathbb {D}\) the answer turns out to be yes.

中文翻译：

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外尔管公式的变化

在1939年外尔表明，球形管的周围紧凑子流形的卷中号的欧氏空间仅取决于该感应黎曼度量中号。对于具有比圆球更一般横截面\(\mathbb {D}\) 的管子，管子体积的这种内在性质是否可以保留？在\(\mathbb {D}\)上足够强的对称条件下，答案是肯定的。