On local congruence of immersions in homogeneous or nonhomogeneous spaces

DOI10.3842/SIGMA.2013.036zbMATH Open1277.53017arXiv1304.7430MaRDI QIDQ352515

Jeongoo Cheh

Publication date: 4 July 2013

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

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 $k^{mth}$ 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 ${mathbbR}^3$ subject to rotations

Full work available at URL: https://arxiv.org/abs/1304.7430

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zbMATH Keywords

congruenceequivariant moving frameinvariant coframe fieldnonhomogeneous space

Mathematics Subject Classification ID

Jets in global analysis (58A20) Local submanifolds (53B25) Differential invariants (local theory), geometric objects (53A55)

Related Items (2)

Locally convex surfaces immersed in a Killing submersion ⋮ Local triviality of the restriction map for immersions with normal crossings: An extension of a result of R. Palais

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