Riemannian Geometry
Edition: 3rd edition
Publisher: Springer-Verlag
Published: November 1997
Format: Paperback
ISBN-13: 9780387563428
Subjects: Riemannian Manifolds; Science/Mathematics
First sentence: 1.1 Definition. A subset M Rn+k is an n-dimensional submanifold of class Cp of Rn+k if, for any x M, there exists a neighborhood U of x in Rn+k and a Cp submersion f : U Rk such that U M = f-1(0) (we recall that f is a submersion if its differential map is surjective at each point).