caa a22 4500 445884371 CHVBK 20180317145554.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s10711-010-9520-9 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9520-9 Partially isometric immersions and free maps [Elektronische Daten] [Giuseppina D'Ambra, Roberto De Leo, Andrea Loi] In this paper we investigate the existence of "partially” isometric immersions. These are maps $${f:M\rightarrow \mathbb{R}^q}$$ which, for a given Riemannian manifold M, are isometries on some sub-bundle $${\mathcal{H}\subset TM}$$. The concept of free maps, which is essential in the Nash-Gromov theory of isometric immersions, is replaced here by that of $${\mathcal{H}}$$ -free maps, i.e. maps whose restriction to $${\mathcal{H}}$$ is free. We prove, under suitable conditions on the dimension q of the Euclidean space, that $${\mathcal{H}}$$ -free maps are generic and we provide, for the smallest possible value of q, explicit expressions for $${\mathcal{H}}$$ -free maps in the following three settings: 1-dimensional distributions in $${\mathbb{R}^2}$$, Lagrangian distributions of completely integrable systems, Hamiltonian distributions of a particular kind of Poisson Bracket. Springer Science+Business Media B.V., 2010 Isometric immersions nationallicence Nash's implicit function theorem nationallicence Free maps nationallicence Distributions nationallicence Completely integrable systems nationallicence Poisson manifolds nationallicence D'Ambra Giuseppina Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut De Leo Roberto Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut Loi Andrea Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 79-95 0046-5755 151:1<79 2011 151 10711 https://doi.org/10.1007/s10711-010-9520-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9520-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- D'Ambra Giuseppina Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 700 1- De Leo Roberto Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 700 1- Loi Andrea Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 151/1(2011-04-01), 79-95 0046-5755 151:1<79 2011 151 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer