|
On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces
Jeongoo Cheh Department of Mathematics & Statistics, The University of Toledo, Toledo, OH 43606, USA
Аннотация:
We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in $G$-spaces, whether homogeneous or not, provided that a certain $k^{\mathrm{th}}$ order jet bundle over the $G$-space admits a $G$-invariant local coframe field of constant structure. As a corollary, we note that the differential order of a minimal complete set of congruence invariants is bounded by $k+1$. We demonstrate the method by rediscovering the speed and curvature invariants of Euclidean planar curves, the Schwarzian derivative of holomorphic immersions in the complex projective line, and equivalents of the first and second fundamental forms of surfaces in $\mathbb{R}^3$ subject to rotations.
Ключевые слова:
congruence; nonhomogeneous space; equivariant moving frame; constant-structure invariant coframe field.
Поступила: 14 мая 2012 г.; в окончательном варианте 19 апреля 2013 г.; опубликована 28 апреля 2013 г.
Образец цитирования:
Jeongoo Cheh, “On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces”, SIGMA, 9 (2013), 036, 21 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma819 https://www.mathnet.ru/rus/sigma/v9/p36
|
Статистика просмотров: |
Страница аннотации: | 161 | PDF полного текста: | 37 | Список литературы: | 47 |
|