Show that there is no immersion of S^n into R^n

  • Thread starter Thread starter hadi amiri 4
  • Start date Start date
hadi amiri 4
Messages
98
Reaction score
1
show that there is no immersion of [/n] into [R][/n]
 
Physics news on Phys.org


show that there is no immersion of S^n into R^n
 


By definition;

f : S^{n}\rightarrow R^n is an immersion if;

D_{p}f : T_{p}S^n \rightarrow T_{f(p)}R^n
 

Similar threads

I SL(n,R) Lie group as submanifold of GL(n,R)
Replies
36
Views
4K
I Induced orientation on boundary of ##\mathbb{H}^n## in ##\mathbb{R}^n##
Replies
6
Views
2K
I Injective immersion that is not a smooth embedding
Replies
7
Views
5K
I Generic Curve in R^n: What We Know
Replies
5
Views
2K
I Prove the following statement about n-Manifolds
Replies
6
Views
2K
I Are Coordinates on a Manifold Really Functions from R^n to R?
Replies
17
Views
3K
A Differential forms on R^n vs. on manifold
Replies
4
Views
2K
Show that ##^{n+1}C_r=^nC_r+^nC_{r-1}##
Replies
14
Views
2K
Prove ##1 + a=s(a)=a+1## for ##a \in \mathbb{N}##
Replies
1
Views
1K
A About computing the tangent space at 1 of certain lie groups
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top