Geodesic
An extremal theorem of Riemannian geometry
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 795-804

Voir la notice de l'article provenant de la source Math-Net.Ru

An exact upper estimate for the volume of a tubular neighborhood of a smooth submanifold $N$ of a complete Riemann space $M$ depending upon the volume of $N$ and lower bound for the sectional curvatures of $M$ is given. If $N$ is a closed geodesic, then the equality is attained in the estimate if and only if $M$ is a generalized lens space. 
@article{MZM_1976_19_5_a14,
     author = {S. V. Buyalo},
     title = {An extremal theorem of {Riemannian} geometry},
     journal = {Matemati\v{c}eskie zametki},
     pages = {795--804},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a14/}
}
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S. V. Buyalo. An extremal theorem of Riemannian geometry. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 795-804. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a14/