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Unit tangent bundle
About: Unit tangent bundle is a research topic. Over the lifetime, 1056 publications have been published within this topic receiving 15845 citations.
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TL;DR: In this paper, the conditions for fundamental singularities when the bundle homomorphism is induced from a Morin map were studied, where the tangent distribution is the contact structure and the singularities were characterized by using the Hamilton vector fields.
Abstract: We consider bundle homomorphisms between tangent distributions and vector bundles of the same rank. We study the conditions for fundamental singularities when the bundle homomorphism is induced from a Morin map. When the tangent distribution is the contact structure, we characterize singularities of the bundle homomorphism by using the Hamilton vector fields.
Posted Content•
27 Oct 2002
TL;DR: In this article, it was shown that on a 4-manifold M endowed with a spin-structure induced by an almost-complex structure, a self-dual spinor field φ ∈ Γ(W) is the same as a bundle morphism φ : TM → TM acting on the fiber by selfdual conformal transformations, such that the Clifford multiplication is just the evaluation of φ on tangent vectors.
Abstract: We show that, on a 4-manifold M endowed with a spin -structure induced by an almost-complex structure, a self-dual (= positive) spinor field φ ∈ Γ(W) is the same as a bundle morphism φ : TM → TM acting on the fiber by self-dual conformal transformations, such that the Clifford multiplication is just the evaluation of φ on tangent vectors, and that the squaring map σ : W → Λ acts by pulling-back the fundamental form of the almost-complex structure. We use this to detect Kähler and symplectic
TL;DR: In this article , the authors studied generalized magnetic vector fields as magnetic maps from a Kählerian manifold to its tangent bundle endowed with a Berger type deformed Sasaki metric.
TL;DR: In this article , the authors define the Mus-Gradient metric on tangent bundle $TM$ by a deformation non-conform of Sasaki metric over an n-dimensional Riemannian manifold.
Abstract: This paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a
deformation non-conform of Sasaki metric over an n-dimensional Riemannian
manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric
and we characterize a new class of proper biharmonic maps. Examples of proper
biharmonic maps are constructed when all of the factors are Euclidean spaces.