Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
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Variational metrics on and the geometry of nonconservative mechanics
Olga Krupková (1994)
Mathematica Slovaca
Variétés de dimension infinie
Nicole Moulis (1969/1970)
Séminaire Bourbaki
Vector curvature of a surface in a Hilbert space and the Gauss theorem.
Borisov, Yu.F. (2000)
Siberian Mathematical Journal
Vector fields on the Sato Grassmannian.
Francisco J. Plaza Martín (2005)
Collectanea Mathematica
An explicit basis of the space of global vector fields on the Sato Grassmannian is computed and the vanishing of the first cohomology group of the sheaf of derivations is shown.
Volume comparison theorem for tubular neighborhoods of submanifolds in Finsler geometry and its applications
Bing-Ye Wu (2014)
Annales Polonici Mathematici
We consider the distance to compact submanifolds and study volume comparison for tubular neighborhoods of compact submanifolds. As applications, we obtain a lower bound for the length of a closed geodesic of a compact Finsler manifold. When the Finsler metric is reversible, we also provide a lower bound of the injectivity radius. Our results are Finsler versions of Heintze-Karcher's and Cheeger's results for Riemannian manifolds.
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