Explicit geodesic graphs on some H-type groups

Dušek, Zdeněk

Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books, (2002), p. [77]-88 / Harvested from

Résumé

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 $Ad (H)$ -invariant vector subspace of $Lie (G)$ such that $Lie (G) = m \oplus Lie (H)$ . A geodesic graph is a map $ξ : m \to Lie (H)$ such that $t \mapsto exp (t (X + ξ (X))) (e H)$ is a geodesic for every $X \in m ∖ {0}$ . 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.

MR MR1972426 | Zbl 1025.53019

EUDML-ID : urn:eudml:doc:219872
Mots clés:

@article{701689,
     title = {Explicit geodesic graphs on some H-type groups},
     booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2002},
     pages = {[77]-88},
     mrnumber = {MR1972426},
     zbl = {1025.53019},
     url = {http://dml.mathdoc.fr/item/701689}
}

Dušek, Zdeněk. Explicit geodesic graphs on some H-type groups, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books,  (2002), pp. [77]-88. http://gdmltest.u-ga.fr/item/701689/