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A Frobenius theorem for corank-1 continuous distributions in dimensions two and three

S. Luzzatto

http://orcid.org/0000-0001-6992-9190

Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste, Italy

E-mail Address: luzzatto@ictp.it

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S. Türeli̇

Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste, Italy

International School for Advanced Studies (SISSA), Via Bonomea 265, Trieste, Italy

E-mail Address: sinatureli@gmail.com

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K. M. War

Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste, Italy

International School for Advanced Studies (SISSA), Via Bonomea 265, Trieste, Italy

E-mail Address: kwar@ictp.it

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https://doi.org/10.1142/S0129167X16500610Cited by:3 (Source: Crossref)

Abstract

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical Frobenius theorem, which says that an involutive $C^{1}$ distribution is uniquely integrable.

Keywords:

AMSC: 57M25, 57M27

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