Conformal paracontact curvature and the local flatness theorem

By Stefan Ivanov, D. Vassilev, Simeon Zamkovoy. 2007

71 citations recorded by the source corpus.

A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature iff the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved through employing a certain symmetric (0,2) tensor. The well known result of Cartan–Chern–Moser giving necessary and sufficient condition a CR-structure to be CR equivalent to a hyperquadric in $${\mathbb{C}^{n+1}}$$ is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic Yamabe equation on the hyperbolic Heisenberg group is shown.

Subfields: Applied Mathematics, Biomedical Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bb64144485575e1170e95dc8532dcb515014e70e

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In Applied Mathematics

1. D. Perrone
2. Giovanni Calvaruso

In Geometry and Topology

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2. Giovanni Calvaruso

Citations in the corpus

• Geometry of $H$-paracontact metric manifolds (2013, background): “Then, any non-degenerate hypersurface in (R, I, g) inherits an integrable para-contact hermitian structure [16].”