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