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On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric
International Electronic Journal of Geometry, 2023Let $(M^{m}, g)$ be a Riemannian manifold and $TM$ its tangent bundle equipped with a deformed Sasaki metric. In this paper, firstly we investigate all forms of Riemannian curvature tensors of $TM$ (Riemannian curvature tensor, Ricci curvature, sectional curvature and scalar curvature).
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A Characterization of Differential Bundles in Tangent Categories
Applied Categorical Structures26 pages, to appear in Applied Categorical Structures, minor changes based on feedback from referee and ...
Michael Ching
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Bundle-like metrics on a tangent bundle
AIP Conference Proceedings, 2010Let (M,g,F) be a semi‐Riemannian manifold with metric g and non‐degenerated foliation F. Let TM = D⊕D⊥ and D⊥ be the intrinsic connection on D⊥. A metric g on M is said to be bundle‐like for the non‐degenerated foliation F if the induced semi‐Riemannian metric on D⊥ is parallel with respect to the intrinsic connection D⊥.Supposing that a Riemannian ...
Stanisław Ewert-Krzemieniewski +4 more
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Tangent Bundles and Tangent Sphere Bundles
2002In the first two sections of this chapter we discuss the geometry of the tangent bundle and the tangent sphere bundle. In Section 3 we briefly present a more general construction on vector bundles and in Section 4 specialize to the case of the normal bundle of a submanifold.
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Electroweak Symmetry on the Tangent Bundle
International Journal of Theoretical Physics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2006
Summary: We study the geometry of manifolds whose tangent bundle is endowed with a Riemannian metric. The Levi-Civita connection, Schouten-Van Kampen connection and Vranceanu connection are the main tools for this study. We obtain characterizations of special classes of vertical foliations and compare the sectional curvatures of the horizontal ...
Al-Aqeel, Adnan, Bejancu, Aurel
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Summary: We study the geometry of manifolds whose tangent bundle is endowed with a Riemannian metric. The Levi-Civita connection, Schouten-Van Kampen connection and Vranceanu connection are the main tools for this study. We obtain characterizations of special classes of vertical foliations and compare the sectional curvatures of the horizontal ...
Al-Aqeel, Adnan, Bejancu, Aurel
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On Projective Manifolds With Pseudo-Effective Tangent Bundle
Journal of the Institute of Mathematics of Jussieu, 2022Masataka Iwai
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Lifts of a Quarter-Symmetric Metric Connection From a Sasakian Manifold to Its Tangent Bundle
Mathematics, 2023Ljubica S Velimirović +2 more
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On the Tangent Bundle of a Grassman Manifold
American Journal of Mathematics, 1964Hsiang, W. C., Szczarba, R. H.
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Linear Connections on Tangent Bundles
Journal of the London Mathematical Society, 1964Yano, K., Ledger, A.
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