Partial immersions and partially free maps

DOI10.1016/J.DIFGEO.2011.04.007zbMATH Open1225.53053arXiv1010.5362OpenAlexW2114600225WikidataQ115356920 ScholiaQ115356920MaRDI QIDQ719815

Roberto De Leo

Publication date: 12 October 2011

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Abstract: In a recent paper~cite{DDL10} we studied basic properties of partial immersions and partially free maps, a generalization of free maps introduced first by Gromov in~cite{Gro70}. In this short note we show how to build partially free maps out of partial immersions and use this fact to prove that the partially free maps in critical dimension introduced in Theorems 1.1-1.3 of~cite{DDL10} for three important types of distributions can actually be built out of partial immersions. Finally, we show that the canonical contact structure on $$ admits partial immersions in critical dimension for every $n$.

Full work available at URL: https://arxiv.org/abs/1010.5362

zbMATH Keywords

distributionsPoisson manifoldscompletely integrable systemspartially free mapspartially isometric immersions

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Jets in global analysis (58A20) Poisson manifolds; Poisson groupoids and algebroids (53D17) Global submanifolds (53C40) Immersions in differential topology (57R42) Vector distributions (subbundles of the tangent bundles) (58A30)

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