Kodai Mathematical Journal

Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations

Tetsuya Ozawa and Hajime Sato

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Abstract

We discuss an equivalence problem of pseudo-Hermitian structures on 3-dimensional manifolds, and develop a method of constructing equivalence maps by using systems of linear partial differential equations. It is proved that a pseudo-Hermitian structure is transformed to a standard model of pseudo-Hermitian structure constructed on the Heisenberg group if and only if it has the vanishing pseudo-Hermitian torsion and the pseudo-Hermitian curvature. A system of linear partial differential equations whose coefficients are associated with a given pseudo-Hermitian structure is introduced, and plays a central role in this paper. The system is integrable if and only if the pseudo-Hermitian structure has vanishing torsion and curvature. The equivalence map is constructed by using a normal basis of the solution space of the system.

Article information

Source
Kodai Math. J., Volume 34, Number 1 (2011), 105-123.

Dates
First available in Project Euclid: 31 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1301576765

Digital Object Identifier
doi:10.2996/kmj/1301576765

Mathematical Reviews number (MathSciNet)
MR2786784

Zentralblatt MATH identifier
1215.58018

Citation

Ozawa, Tetsuya; Sato, Hajime. Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations. Kodai Math. J. 34 (2011), no. 1, 105--123. doi:10.2996/kmj/1301576765. https://projecteuclid.org/euclid.kmj/1301576765


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