Conformal paracontact curvature and the local flatness theorem. (English) Zbl 1195.53048
In this paper the authors find a tensor invariant characterizing locally the integrable para-contact Hermitian structures which are para-contact conformally equivalent to the flat structure on the hyperbolic Heisenberg group. To any integrable para-contact Hermitian structure the authors associate a curvature -type tensor \(W^{pc}\), called para-contact conformal curvature, defined in terms of the curvature and torsion of the canonical connection. It is proved that the \(W^{pc}\) of an integrable para-contact Hermitian manifold \((M, \eta)\) is invariant under para-contact conformal transformations. Necessary and sufficient conditions for \((M,\eta)\) to locally para-contact conformal to the hyperboloid \(HS^{2n+1}\) are proved. Finally, the authors show an explicit formula for the regular part of solutions of the Yamabe equation.
Reviewer: Gabriela Paola Ovando (Rosario)
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
Keywords:
paracontact; CR structures; pseudo-conformal flat; paracontact conformally invariant curvature; Cartan-Chern-Moser theoremReferences:
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