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Zagane, Abderrahim

Vertical rescaled berger deformation metric on the tangent bundle. (English) Zbl 1513.53056

Trans. Natl. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci. 41, No. 4, Math., 166-180 (2021).
Summary: In this paper, we introduce the vertical rescaled berger deformation metric on the tangent bundle \(T M\) over an anti-paraKähler manifold \((M^{2m}, \varphi, g)\) as a new natural metric with respect tog non-rigid on \(T M\). Firstly, we investigate the Levi-Civita connection of this metric, Secondly we study the curvature tensor and also we characterize the scalar curvature.

Cited in 2 Documents

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53B35 Local differential geometry of Hermitian and Kählerian structures
53A45 Differential geometric aspects in vector and tensor analysis

Keywords:

horizontal lift; vertical lift; cotangent bundles; vertical rescaled berger deformation metric; curvature tensor
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References:

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