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 language | English |
|---|---|
| Pages (from-to) | 117-131 |
| Number of pages | 15 |
| Journal | Geometriae Dedicata |
| Volume | 154 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Oct 1 2011 |
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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 journal › Article
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TY - JOUR
T1 - Curves in homogeneous spaces and their contact with 1-dimensional orbits
AU - do Nascimento, Vanderlei M.
AU - Saeki, Osamu
PY - 2011/10/1
Y1 - 2011/10/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80052288213&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052288213&partnerID=8YFLogxK
U2 - 10.1007/s10711-010-9571-y
DO - 10.1007/s10711-010-9571-y
M3 - Article
AN - SCOPUS:80052288213
VL - 154
SP - 117
EP - 131
JO - Geometriae Dedicata
JF - Geometriae Dedicata
SN - 0046-5755
IS - 1
ER -