TY - JOUR
T1 - Curves in homogeneous spaces and their contact with 1-dimensional orbits
AU - do Nascimento, Vanderlei M.
AU - Saeki, Osamu
N1 - Funding Information:
The second author has been partially supported by Grant-in-Aid for Scientific Research (No. 19340018), Japan Society for the Promotion of Science.
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/10
Y1 - 2011/10
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.
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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 -