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

Cruceanu, Vasile; Etayo, Fernando

Algebras Groups Geom. 16, No. 1, 47-61 (1999).

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.

Reviewer: Thalia D.Jeffres (Morelia)

MSC:

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

Keywords:

para-Hermitian structures