Artículos de revistas
Homogeneous geodesics in pseudo-Riemannian nilmanifolds
Fecha
2016-04Registro en:
del Barco, Viviana Jorgelina; Homogeneous geodesics in pseudo-Riemannian nilmanifolds; De Gruyter; Advances In Geometry; 16; 2; 4-2016; 1-18
1615-715X
1615-7168
CONICET Digital
CONICET
Autor
del Barco, Viviana Jorgelina
Resumen
We study the geodesic orbit property for nilpotent Lie groups N when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When N acts on itself by left-translations we show that it is a geodesic orbit space if and only if the metric is bi-invariant. Assuming N is 2-step nilpotent and with non-degenerate center we give algebraic conditions on the Lie algebra n of N in order to verify that every geodesic is the orbit of a one-parameter subgroup of N ⋊ Auto(N). In addition we present an example of an almost g.o. space such that for null homogeneous geodesics, the natural parameter of the orbit is not always the affine parameter of the geodesic.