The curvature of the Sasaki metric of tangent sphere bundles

1990 ◽  
Vol 48 (1) ◽  
pp. 108-117
Author(s):  
A. L. Yampol'ski�
Keyword(s):  
Sasaki Metric ◽  
Tangent Sphere

Geodesics on the unit tangent bundle

2003 ◽  
Vol 133 (6) ◽  
pp. 1209-1229 ◽  
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.

On the non-regularity of tangent sphere bundles

1978 ◽  
Vol 82 (1-2) ◽  
pp. 13-17 ◽  
Author(s):  
David E. Blair
Keyword(s):  
Riemannian Manifold ◽  
Large Class ◽  
Constant Curvature ◽  
Positive Constant ◽  
Contact Structure ◽  
Compact Riemannian Manifold ◽  
Contact Structures ◽  
Sphere Bundle ◽  
Contact Manifolds ◽  
Tangent Sphere

SynopsisClassically the tangent sphere bundles have formed a large class of contact manifolds; their contact structures are not in general regular, however. Specifically we prove that the natural contact structure on the tangent sphere bundle of a compact Riemannian manifold of non-positive constant curvature is not regular.

scholarly journals On Geodesics of Warped Sasaki Metric

2017 ◽  
Vol 5 (1) ◽  
pp. 85-92
Author(s):  
Abderrahim ZAGANE ◽  
Mustapha DJAA
Keyword(s):  
Sasaki Metric

scholarly journals N-Legendre and N-slant curves in the unit tangent bundle of Minkowski surfaces

2017 ◽  
Vol 11 (01) ◽  
pp. 1850008 ◽  
Author(s):  
Murat Bekar ◽  
Fouzi Hathout ◽  
Yusuf Yayli
Keyword(s):  
Tangent Bundle ◽  
Inner Product ◽  
Normal Vector ◽  
Sasaki Metric ◽  
Reeb Vector ◽  
Nonzero Constant ◽  
Unit Tangent Bundle ◽  
Slant Curves

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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