On Geodesics of Warped Sasaki Metric

Let [Formula: see text] be a unit tangent bundle of Minkowski surface [Formula: see text] endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in [Formula: see text] and several important characterizations of these curves are given.

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The Geometry of the Sasaki Metric on the Sphere Bundles of Euclidean Atiyah Vector Bundles

Mediterranean Journal of Mathematics ◽

10.1007/s00009-020-01614-3 ◽

2020 ◽

Vol 17 (6) ◽

Author(s):

Mohamed Boucetta ◽

Hasna Essoufi

Keyword(s):

Vector Bundles ◽

Sasaki Metric

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The super-Sasaki metric on the antitangent bundle

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820501224 ◽

2020 ◽

Vol 17 (08) ◽

pp. 2050122

Author(s):

Andrew James Bruce

Keyword(s):

Riemannian Manifold ◽

Tangent Bundle ◽

Symplectic Form ◽

Riemannian Metric ◽

Riemannian Structure ◽

Sasaki Metric

We show how to lift a Riemannian metric and almost symplectic form on a manifold to a Riemannian structure on a canonically associated supermanifold known as the antitangent or shifted tangent bundle. We view this construction as a generalization of Sasaki’s construction of a Riemannian metric on the tangent bundle of a Riemannian manifold.

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The curvature of the Sasaki metric of tangent sphere bundles

Journal of Soviet Mathematics ◽

10.1007/bf01098055 ◽

1990 ◽

Vol 48 (1) ◽

pp. 108-117

Author(s):

A. L. Yampol'ski�

Keyword(s):

Sasaki Metric ◽

Tangent Sphere

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Geodesics on the unit tangent bundle

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500002882 ◽

2003 ◽

Vol 133 (6) ◽

pp. 1209-1229 ◽

Cited By ~ 6

Author(s):

J. Berndt ◽

E. Boeckx ◽

P. T. Nagy ◽

L. Vanhecke

Keyword(s):

Riemannian Manifold ◽

Vector Field ◽

Tangent Bundle ◽

Unit Vector ◽

Sphere Bundle ◽

Sasaki Metric ◽

Tangent Sphere Bundle ◽

Tangent Sphere ◽

Unit Tangent Bundle ◽

Unit Tangent Sphere Bundle

A geodesic γ on the unit tangent sphere bundle T1M of a Riemannian manifold (M, g), equipped with the Sasaki metric gS, can be considered as a curve x on M together with a unit vector field V along it. We study the curves x. In particular, we investigate for which manifolds (M, g) all these curves have constant first curvature κ1 or have vanishing curvature κi for some i = 1, 2 or 3.

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Lifts of connections to the bundle of (1,1) type tensor frames

Sigma Journal of Engineering and Natural Sciences – Sigma Mühendislik ve Fen Bilimleri Dergisi ◽

10.14744/sigma.2021.00007 ◽

2021 ◽

pp. 177-183

Author(s):

Habil FATTAYEV

Keyword(s):

Smooth Manifold ◽

Linear Connection ◽

Sasaki Metric ◽

Geodesic Lines ◽

Complete Lift

In this paper we consider the bundle of (1,1) type tensor frames over a smooth manifold, define the horizontal and complete lifts of symmetric linear connection into this bundle. Also we study the properties of the geodesic lines corresponding to the complete lift of the linear connection and investigate the relations between Sasaki metric and lifted connections on the bundle of (1,1) type tensor frames.

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