Explicit geodesic graphs on some H-type groups

Dušek, Zdeněk. "Explicit geodesic graphs on some H-type groups." Proceedings of the 21st Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2002. [77]-88. <http://eudml.org/doc/219872>.

@inProceedings{Dušek2002,
abstract = {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 geodesic graph is a map $\xi :m\rightarrow \text\{Lie\}(H)$ such that \[ t\mapsto \exp (t(X+\xi (X)))(eH) \] is a geodesic for every $X\in m\setminus \lbrace 0\rbrace $. 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.},
author = {Dušek, Zdeněk},
booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {[77]-88},
publisher = {Circolo Matematico di Palermo},
title = {Explicit geodesic graphs on some H-type groups},
url = {http://eudml.org/doc/219872},
year = {2002},
}

TY - CLSWK
AU - Dušek, Zdeněk
TI - Explicit geodesic graphs on some H-type groups
T2 - Proceedings of the 21st Winter School "Geometry and Physics"
PY - 2002
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [77]
EP - 88
AB - 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 geodesic graph is a map $\xi :m\rightarrow \text{Lie}(H)$ such that \[ t\mapsto \exp (t(X+\xi (X)))(eH) \] is a geodesic for every $X\in m\setminus \lbrace 0\rbrace $. 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.
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/219872
ER -