On almost para-Hermitian manifolds. (English) Zbl 1003.53024

Let \(M\) be a manifold with an almost para-Hermitian structure. The first result of this paper is to define and prove the existence of a unique canonical connection. This connection lends itself naturally to the characterization of certain distinguished almost para-Hermitian structures. There is also a “natural” connection derived from the Levi-Civita connection, and a condition under which these coincide is given. The paper concludes with an example in which the authors construct an almost para-Hermitian structure on the tangent bundle of a (pseudo-) Riemannian manifold.


53C05 Connections (general theory)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)