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2012•Taiwanese Journal of MathematicsOpen access

GENERAL NATURAL RIEMANNIAN ALMOST PRODUCT AND PARA-HERMITIAN STRUCTURES ON TANGENT BUNDLES

Simona-Luiza Druţă-Romaniuc

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Abstract

We find the almost product (locally product) structures of general natural lift type on the tangent bundle of a Riemannian manifold. We get the conditions under which the tangent bundle endowed with such a structure and with a general natural lifted metric is a Riemannian almost product (locally product) or an (almost) para-Hermitian manifold. We give a characterization of the general natural (almost) para-Hermitian structures, which are (almost) para-Kählerian on the tangent bundle.

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We find the almost product (locally product) structures of general natural lift type on the tangent bundle of a Riemannian manifold. We get the conditions under which the tangent bundle endowed with such a structure and with a general natural lifted metric is a Riemannian almost product (locally product) or an (almost) para-Hermitian manifold. We give a characterization of the general natural (almost) para-Hermitian structures, which are (almost) para-Kählerian on the tangent bundle.

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Available abstract

We find the almost product (locally product) structures of general natural lift type on the tangent bundle of a Riemannian manifold. We get the conditions under which the tangent bundle endowed with such a structure and with a general natural lifted metric is a Riemannian almost product (locally product) or an (almost) para-Hermitian manifold. We give a characterization of the general natural (almost) para-Hermitian structures, which are (almost) para-Kählerian on the tangent bundle.

Key concepts: Tangent bundle, Hermitian manifold, Mathematics, Unit tangent bundle, Hermitian matrix, Pure mathematics, Product (mathematics), Tangent

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