Let be the (n+1)-dimensional threadlike Lie group,
an arbitrary closed connected Lie subgroup of
and
an abelian discontinuous group for the homogeneous space
. We provide in this work an explicit description of the parameter space
and of the deformation space
in the particular case where
. Furthermore we discuss the local rigidity of
and make a link with the Baklouti conjecture. This paper provides, through a concrete case study, a gentle initiation to the theory of deformations of Lie group actions
Milestones:
Received: October 2015
Published online: June 2016
Authors:
Fatma KhlifDepartment of Mathematics,
Faculty of Sciences at Sfax,
Sfax University,
Route de Soukra, 1171, Sfax, Tunisia