Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations
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- Ozawa Tetsuya
- Department of Mathematics Meijo University
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- Sato Hajime
- Graduate School of Mathematics Nagoya University
Description
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.
Journal
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- Kodai Mathematical Journal
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Kodai Mathematical Journal 34 (1), 105-123, 2011
Department of Mathematics, Tokyo Institute of Technology
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Keywords
Details 詳細情報について
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- CRID
- 1390001205272370816
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- NII Article ID
- 130004496128
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- ISSN
- 18815472
- 03865991
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- MRID
- 2786784
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
- KAKEN
- OpenAIRE
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- Abstract License Flag
- Disallowed
