On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9, випуск за цей рік
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dc.contributor.author	Cheh, J.
dc.date.accessioned	2019-02-19T18:27:40Z
dc.date.available	2019-02-19T18:27:40Z
dc.date.issued	2013
dc.identifier.citation	On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces / J. Cheh // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 53A55; 53B25
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2013.036
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149192
dc.description.abstract	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 kth 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 R³ subject to rotations.	uk_UA
dc.description.sponsorship	This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. This work has benefited from the discussions held in the Dif ferential Geometry and Lie Theory seminars at the University of Toledo; the author would like to thank the organizers and participants of the seminars. Also, the anonymous referees’ critical and yet helpful comments have contributed significantly in the process of revising and improving the paper; the author is very grateful to the referees. It is hoped that this work serves to reflect, although only to a small extent limited by the author’s meager knowledge, the author’s appreciation of the introduction by Professor Peter Olver to the marvelous unifying philosophy and technology of symmetry, invariance, and equivalence.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA