Submanifolds of R^s Flashcards
1
Q
n-dimensional submanifold M in R^s
A
for all points in M, there exists an open neighbourhood and an open U’ in R^n such that φ: U’ to U is a diffeomorphism
2
Q
regular value q
A
domain open and f differentiable, f^(-1)(q)=p, and Dfp is surjective
3
Q
tangent vector
A
there is a smooth curve γ from (-ε,ε) to M such that γ(0)=p and γ’(0)=v
4
Q
tangent space
A
set of all tangent vectors to M at p
5
Q
derivative of function between submanifolds
A
Dfp: TpM –> Tf(p)N sending γ’(0) to (f ο γ)’(0)
6
Q
local diffeomorphism
A
for all p, Dfp is an isomorphism
7
Q
immersion
A
Dfp is injective
8
Q
submersion
A
Dfp is surjective
