Curves in homogeneous spaces and their contact with 1-dimensional orbits

Vanderlei M. do Nascimento, Osamu Saeki

Research output: Contribution to journalArticle

Abstract

Let α be a C curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace Skα of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose orbit through x has contact of order k with α. In this paper, we give various important properties of the sequence of subspaces G ⊃ S1α ⊃ S2α ⊃ S3α. In particular, we give a stabilization property for certain well-behaved curves. We also describe its relationship to the isotropy subgroup with respect to the contact element of order k associated with α.

Original languageEnglish
Pages (from-to)117-131
Number of pages15
JournalGeometriae Dedicata
Volume154
Issue number1
DOIs
Publication statusPublished - Oct 1 2011

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Homogeneous Space
Orbit
Contact
Curve
Subspace
Subgroup
Isotropy
Lie Algebra
Stabilization

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Cite this

Curves in homogeneous spaces and their contact with 1-dimensional orbits. / do Nascimento, Vanderlei M.; Saeki, Osamu.

In: Geometriae Dedicata, Vol. 154, No. 1, 01.10.2011, p. 117-131.

Research output: Contribution to journalArticle

do Nascimento, Vanderlei M. ; Saeki, Osamu. / Curves in homogeneous spaces and their contact with 1-dimensional orbits. In: Geometriae Dedicata. 2011 ; Vol. 154, No. 1. pp. 117-131.
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