Notes on the tangent bundle with deformed complete lift metric
Aydin Gezer,Mustafa Özkan +1 more
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In this article, the authors studied the properties of the tangent bundle with a deformed complete lift metric, and showed that the deformed lift metric can be used to study the manifold properties of tangent bundles.Abstract:
In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.read more
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A classification of conformal vector fields on the tangent bundle
Zohre Raei,Dariush Latifi +1 more
TL;DR: In this article, a classification of infinitesimal fibre-preserving conformal transformations on the tangent bundle of a Riemannian manifold is given. But the classification is restricted to conformal transformation on a manifold.
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Infinitesimal Affine Transformations and Mutual Curvatures on Statistical Manifolds and Their Tangent Bundles
TL;DR: In this article , the authors studied the dualistic structure of the tangent bundle of a statistical manifold M and its tangent manifold TM and obtained the mutual curvatures of the complete, horizontal, and Sasaki connections.
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Derivatives with respect to horizontal and vertical lifts of the deformed complete lift metric G_{f} on tangent bundle.
Haşim Çayir,Rabia ÇAKAN AKPINAR +1 more
TL;DR: In this paper , the deformed complete lift metric on tangent bundle is defined, which is completely determined by its action on vector fields of type X^{H} and ω^{V}.
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IFHP Transformations on the Tangent Bundle with the Deformed Complete Lift Metric
TL;DR: Morevore et al. as mentioned in this paper proved that every holomorphically projective transformation on a Riemannian manifold can be reduced to an affine transformation on the complete lift metric.
References
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Tangent and cotangent bundles
TL;DR: In this article, the authors consider the problem of finding an isomorphism in a set of subsets of a TM and show that there exists a neighborhood W 1, W 2, W 3 of (p, Xp), (p); F ( Xp) and F (Xp) respectively such that W 1 is an open set.
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TL;DR: In this paper, the curvature tensor of the Riemannian space (TM, Tg) corresponding to (If, g) is computed, and it is shown that the space is not Symmetrie unless (M, g, tg) is locally euclidean.
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Riemannian Metrics on Tangent Bundles
TL;DR: Some natural metrics on the tangent and on the sphere tangent bundle of Riemannian manifold were constructed and studied via the moving frame method in this article, and some natural metrics were constructed on the manifold manifold on the basis of these metrics.