Vertical and complete lifts from a manifold to its cotangent bundle

Yano, Kentarô; Patterson, E. M.

doi:10.2969/jmsj/01910091

Cited by 48 publications

(39 citation statements)

References 10 publications

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“…The BNW lift can be obtained by standard symplectification, see e.g. [10], of the complete lift of ∇ to T * Q in the sense of Yano and Patterson [78]. This was observed in [64] and has also been proved in [68].…”

Section: Lift Of the Levi-civita Connectionmentioning

confidence: 71%

Deformation Quantization and Homological Reduction of a Lattice Gauge Model

Pflaum

Rudolph

Schmidt

2021

Commun. Math. Phys.

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For a compact Lie group G we consider a lattice gauge model given by the G-Hamiltonian system which consists of the cotangent bundle of a power of G with its canonical symplectic structure and standard moment map. We explicitly construct a Fedosov quantization of the underlying symplectic manifold using the Levi-Civita connection of the Killing metric on G. We then explain and refine quantized homological reduction for the construction of a star product on the symplectically reduced space in the singular case. Afterwards we show that for G = SU(2) the main hypotheses ensuring the method of quantized homological reduction to be applicable hold in the case of our lattice gauge model. For that case, this implies that the-in general singular-symplectically reduced phase space of the corresponding lattice gauge model carries a star product.

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Section: Lift Of the Levi-civita Connectionmentioning

confidence: 71%

Deformation Quantization and Homological Reduction of a Lattice Gauge Model

Pflaum

Rudolph

Schmidt

2021

Commun. Math. Phys.

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“…Also, the idea of F structure manifold on a di¤erentiable manifold developed by Yano [14], Ish¬hara and Yano [7], Goldberg [6] and among others. Moreover, Yano and Patterson [15,16] studied on the horizontal and complete lifts from a di¤erentiable manifold M n of class C 1 to its cotangent bundles. Andreu has studied the structure de…ned by a tensor …eld F (6 = 0) of type (1; 1) satisfying F 5 + F = 0 [1].…”

Section: Introductionmentioning

confidence: 99%

On the lifts of F_{a}(5,1)-structure on tangent and cotangent bundle

Jabrailzade¹

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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This paper consist of three main sections. In the …rst part, we obtain the complete lifts of the Fa(5; 1) structure on tangent bundle. We have also obtained the integrability conditions by calculating the Nijenhuis tensors of the complete lifts of Fa(5; 1) structure. Later we get the conditions of to be the almost holomor…c vector …eld with respect to the complete lifts of Fa(5; 1) structure. Finally, we obtained the results of the Tachibana operator applied to the vector …elds with respect to the complete lifts of Fa(5; 1) structure on tangent bundle. In the second part, all results obtained in the …rst section investigated according to the horizontal lifts of Fa(5; 1) structure in tangent bundle T (M n ). In …nally section, all results obtained in the …rst and second section were investigated according to the horizontal lifts of the Fa(5; 1) structure in cotangent bundle T (M n ).

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“…where , XY are vector field and   , XY is the Lie bracket of vector fields. The torsion tensors are studied on cotangent bundle of a manifold by many authors (Yano and Patterson, 1967;Mok, 1977).…”

Section: Introductionmentioning

confidence: 99%

Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle

Akpinar

2020

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In this study, the geodesics and torsion tensor according to g-lift of Riemannian connection  on cotangent bundle * are investigated. Firstly, using the components of g-lift of Riemannian connection  on cotangent bundle * the components of torsion tensor according to glift of Riemannian connection  are obtained. So the torsion tensor according to g-lift of Riemannian connection  are determined. Finally, geodesics on cotangent bundle * according to g-lift of Riemannian connection  are studied.

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Vertical and complete lifts from a manifold to its cotangent bundle

Cited by 48 publications

References 10 publications

Deformation Quantization and Homological Reduction of a Lattice Gauge Model

Deformation Quantization and Homological Reduction of a Lattice Gauge Model

On the lifts of F_{a}(5,1)-structure on tangent and cotangent bundle

Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle

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