Elliptic geometry in 3 dimensions

TrickyDicky
Messages
3,507
Reaction score
28
I'm interested in elliptic space from an intrinsic point of view(manifold pov) rather than the models based in Euclidean embeddings.
Would it be correct to say that the isometry group of this geometry is isomorphic to SU(2), i.e.:versors or unit quaternions?
 
Physics news on Phys.org
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Thread 'Injective immersion and embedding'

Hello! There is a simple line in the textbook. If ##S## is a manifold, an injectively immersed submanifold ##M## of ##S## is embedded if and only if ##M## is locally closed in ##S##. Recall the definition. M is locally closed if for each point ##x\in M## there open ##U\subset S## such that ##M\cap U## is closed in ##U##. Embedding to injective immesion is simple. The opposite direction is hard. Suppose I have ##N## as source manifold and ##f:N\rightarrow S## is the injective...
View full post »

Similar threads

I Pseudo-Riemaniann isometries
Replies
4
Views
2K
I 2-sphere manifold intrinsic definition
Replies
44
Views
5K
I What are the restrictions when swapping between geometries in physics?
Replies
12
Views
3K
B Is my intuitive way of thinking about non-Euclidean geometry valid?
Replies
19
Views
3K
Local parameterizations and coordinate charts
Replies
14
Views
4K
I The standard model from loop quantum gravity via spinors octonions
Replies
26
Views
4K
I Ads/CFT and Ashtekar variables or spinfoam
Replies
7
Views
3K
A A question about coordinate distance & geometrical distance
Replies
13
Views
2K
Very elementary differential geometry questions
Replies
7
Views
4K
A Defining a Contact Structure Globally -- Obstructions?
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top