caa a22 4500 445883995 CHVBK 20180317145553.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10711-010-9571-y doi (NATIONALLICENCE)springer-10.1007/s10711-010-9571-y Curves in homogeneous spaces and their contact with 1-dimensional orbits [Elektronische Daten] [Vanderlei do Nascimento, Osamu Saeki] Let α be a C ∞ curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace $${S^{\alpha}_k}$$ of the Lie algebra $${\mathcal{G}}$$ 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 $${\mathcal{G} \supset S^{\alpha}_1 \supset S^{\alpha}_2 \supset S^{\alpha}_3 \supset \cdots}$$ . 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. Springer Science+Business Media B.V., 2011 Contact nationallicence Homogeneous space nationallicence Lie group nationallicence 1-parameter subgroup nationallicence Lie algebra nationallicence do Nascimento Vanderlei Departamento de Matemática, IGCE-UNESP, 13500-230, Rio Claro, SP, Brazil aut Saeki Osamu Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, 819-0395, Fukuoka, Japan aut Geometriae Dedicata Springer Netherlands 154/1(2011-10-01), 117-131 0046-5755 154:1<117 2011 154 10711 https://doi.org/10.1007/s10711-010-9571-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9571-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- do Nascimento Vanderlei Departamento de Matemática, IGCE-UNESP, 13500-230, Rio Claro, SP, Brazil aut NATIONALLICENCE 700 1- Saeki Osamu Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, 819-0395, Fukuoka, Japan aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 154/1(2011-10-01), 117-131 0046-5755 154:1<117 2011 154 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer