I'm trying to find a formal definition of a complex hyperbolic space that is $CH^n$.
Can anyone help me please? I tried looking online already but no formal direct definition.
Asked
Active
Viewed 61 times
0
-
Does this answer your question? Definition of complex hyperbolic geometry – Lee Mosher May 13 '20 at 16:03
-
no it does not but thank you – MOULI Kawther May 13 '20 at 16:26
-
Perhaps, if you followed the links in the answer found there, you would also find the formal direct definition that you seek. – Lee Mosher May 13 '20 at 23:06
-
I did already, I didn't find a direct definition – MOULI Kawther May 13 '20 at 23:36
-
I'm familiar with the definition in terms of the unitary group, but I want a more explicit definition if possible – MOULI Kawther May 13 '20 at 23:37
-
it is also known to be the dual of the projective complex space $CP^n$ – MOULI Kawther May 14 '20 at 00:18
-
Then you should probably explain what you mean by a "direct definition", and what it is about those definitions that violate your concept of a "direct definition". Without that, your question is pretty vague. – Lee Mosher May 14 '20 at 02:01
-
Here is a definition (or a characterization): it is a simply connected complete Kaehler manifold with constant negative holomorphic sectional curvature. – Didier Mar 22 '22 at 21:04