arXiv Open Access 2020

Existence of Horizontal Immersions in Fat Distributions

Aritra Bhowmick Mahuya Datta

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Abstrak

Contact structures, as well as their holomorphic and quaternionic counterparts are the primary examples of strongly bracket generating (or fat) distributions. In this article we associate a numerical invariant to corank $2$ fat distribution on manifolds, referred to as \emph{degree} of the distribution. The real distribution underlying a holomorphic contact structure is of degree $2$. Using Gromov's sheaf theoretic and analytic techniques of $h$-principle, we prove the existence of horizontal immersions of an arbitrary manifold into degree $2$ fat distributions and the quaternionic contact structures. We also study immersions of a contact manifold inducing the given contact structure.

Topik & Kata Kunci

math.DG

Penulis (2)

Aritra Bhowmick

Mahuya Datta

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APA MLA BibTeX

Bhowmick, A., Datta, M. (2020). Existence of Horizontal Immersions in Fat Distributions. https://arxiv.org/abs/2007.02058

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓