An almost Complex Structure with Norden Metric on the Phase Space

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International Electronic Journal of Geometry
Volume:16 Issue:1
An almost Complex Structure with Norden Metric on the Phase Space

An almost Complex Structure with Norden Metric on the Phase Space

Authors : Cornelialivia BEJAN, Galia NAKOVA

Pages : 412-416

Doi:10.36890/iejg.1278651

View : 54 | Download : 7

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :On the total space of the cotangent bundle of a Riemannian manifold, we construct a semi-Riemannian metric $G$, with respect to which an almost complex structure $J$ introduced by Oproiu and Poro\\cb{s}niuc is self-adjoint. The structure $insert ignore into journalissuearticles values(J,G);$ turnes out to be an almost complex structure with Norden metric insert ignore into journalissuearticles values(this notion is known in the literature from Norden\`s papers);. The semi-Riemannian context is different from the Riemannian one, as it is pointed out by Duggal and Bejancu in their monograph. We study this structure and provide some necessary and sufficient conditions for it to be a K\\\`ahler structure with Norden metric.
Keywords : almost complex structure, Norden metric, cotangent bundle

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