Summary: Geodesics and curvature of semidirect product groups with right invariant metrics are determined. In the special case of an isometric semidirect product, the curvature is shown to be the sum of the curvature of the two groups. A series of examples, like the magnetic extension of a group, are then considered.
@article{701679,
title = {Geodesics and curvature of semidirect product groups},
booktitle = {Proceedings of the 20th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2001},
pages = {199-206},
mrnumber = {MR1826692},
zbl = {1002.58008},
url = {http://dml.mathdoc.fr/item/701679}
}
Vizman, Cornelia. Geodesics and curvature of semidirect product groups, dans Proceedings of the 20th Winter School "Geometry and Physics", GDML_Books, (2001), pp. 199-206. http://gdmltest.u-ga.fr/item/701679/