| Title:
|
Explicit geodesic graphs on some H-type groups (English) |
| Author:
|
Dušek, Zdeněk |
| Language:
|
English |
| Journal:
|
Proceedings of the 21st Winter School "Geometry and Physics" |
| Volume:
|
|
| Issue:
|
2001 |
| Year:
|
|
| Pages:
|
[77]-88 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A homogeneous Riemannian manifold $M=G/H$ is called a ``g.o. space'' if every geodesic on $M$ arises as an orbit of a one-parameter subgroup of $G$. Let $M=G/H$ be such a ``g.o. space'', and $m$ an $\text{Ad}(H)$-invariant vector subspace of $\text{Lie}(G)$ such that $\text{Lie}(G)=m\oplus\text{Lie}(H)$. A {\sl geodesic graph} is a map $\xi:m\to\text{Lie}(H)$ such that $$ t\mapsto \exp(t(X+\xi(X)))(eH) $$ is a geodesic for every $X\in m\setminus\{0\}$. The author calculates explicitly such geodesic graphs for certain special 2-step nilpotent Lie groups. More precisely, he deals with ``generalized Heisenberg groups'' (also known as ``H-type groups'') whose center has dimension not exceeding three. (English) |
| MSC:
|
22E25 |
| MSC:
|
53C22 |
| MSC:
|
53C30 |
| idZBL:
|
Zbl 1025.53019 |
| idMR:
|
MR1972426 |
| . |
| Date available:
|
2009-07-13T21:46:56Z |
| Last updated:
|
2012-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/701689 |
| . |
