Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations
Tetsuya OzawaHajime Sato
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2011 年 34 巻 1 号 p. 105-123

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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.
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© 2011 Department of Mathematics, Tokyo Institute of Technology
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