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

 Kodai Mathematical Journal

Kodai Mathematical Journal 34(1), 105123, 2011
Department of Mathematics, Tokyo Institute of Technology