Product and anti-Hermitian structures on the tangent space

Details Product and anti-Hermitian structures on the tangent space Product and anti-Hermitian structures on the tangent space

2007-10-20

arxiv.org/abs/0710.3825v1

Mathematics

Differential Geometry

Scientific paper

Noting that the complete lift of a Rimannian metric defined on a differentiable manifold is not 0-homogeneous on the fibers of the tangent bundle . In this paper we introduce a new lift which is 0-homogeneous. It determines on slit tangent bundle a pseudo-Riemannian metric, which depends only on the metric . We study some of the geometrical properties of this pseudo-Riemannian space and define the natural almost complex structure and natural almost product structure which preserve the property of homogeneity and find some new results.

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