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Vanhecke–Willmore conjecture on tube formulas and D'Atri spaces
Vanhecke–Willmore conjecture. If the displayed tube-volume identity holds for every arbitrary unit-speed curve $\gamma$ , then $M$ is a D'Atri space.
Conjectureopend-attri-spaces riemannian-geometry tube-formulasarXiv posted 2 days ago

Vanhecke–Willmore conjecture on tube formulas and D'Atri spaces