scholarly journals Geodesics and Killing vector fields on the tangent sphere bundle

1998 ◽  
Vol 151 ◽  
pp. 91-97 ◽  
Author(s):  
Tatsuo Konno ◽  
Shukichi Tanno
Keyword(s):  
Vector Field ◽  
Constant Curvature ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Sphere Bundle ◽  
Tangent Sphere Bundle ◽  
Tangent Sphere ◽  
Space Of Constant Curvature ◽  
Unit Tangent Sphere Bundle

Abstract.We show that any Killing vector field on the unit tangent sphere bundle with Sasaki metric of a space of constant curvature k ≠ 1 is fiber preserving by studying some property of geodesies on the bundle. As a consequence, any Killing vector field on the unit tangent sphere bundle of a space of constant curvature k ≠ 1 can be extended to a Killing vector field on the tangent bundle.

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.

scholarly journals New application of the Killing vector field formalism: modified periodic potential and two-level profiles of the axionic dark matter distribution

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
Alexander B. Balakin ◽  
Dmitry E. Groshev
Keyword(s):  
Dark Matter ◽  
Vector Field ◽  
Electric Fields ◽  
Vector Fields ◽  
Periodic Potential ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Covariant Model ◽  
Axion Field ◽  
Field Formalism

Abstract We consider the structure of halos of the axionic dark matter, which surround massive relativistic objects with static spherically symmetric gravitational field and monopole-type magneto-electric fields. We work with the model of pseudoscalar field with the extended periodic potential, which depends on additional arguments proportional to the moduli of the Killing vectors; in our approach they play the roles of model guiding functions. The covariant model of the axion field with this modified potential is equipped with the extended formalism of the Killing vector fields, which is established in analogy with the formalism of the Einstein–Aether theory, based on the introduction of a unit timelike dynamic vector field. We study the equilibrium state of the axion field, for which the extended potential and its derivative vanish, and illustrate the established formalism by the analysis of two-level axionic dark matter profiles, for which the stage delimiters relate to the critical values of the modulus of the timelike Killing vector field.

SURFACES IN 𝔼3MAKING CONSTANT ANGLE WITH KILLING VECTOR FIELDS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250023 ◽  
Author(s):  
MARIAN IOAN MUNTEANU ◽  
ANA IRINA NISTOR
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Killing Vector Fields ◽  
Curves And Surfaces ◽  
Constant Angle ◽  
Constant Angle Surfaces

In the present paper we classify curves and surfaces in Euclidean 3-space which make constant angle with a certain Killing vector field. Moreover, we characterize the catenoid and Dini's surface in terms of constant angle surfaces.

scholarly journals On Jacobi-Type Vector Fields on Riemannian Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1139 ◽  
Author(s):  
Bang-Yen Chen ◽  
Sharief Deshmukh ◽  
Amira A. Ishan
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Compact Riemannian Manifold ◽  
Killing Vector ◽  
Sufficient Conditions ◽  
Killing Vector Field ◽  
Natural Question ◽  
Necessary And Sufficient

In this article, we study Jacobi-type vector fields on Riemannian manifolds. A Killing vector field is a Jacobi-type vector field while the converse is not true, leading to a natural question of finding conditions under which a Jacobi-type vector field is Killing. In this article, we first prove that every Jacobi-type vector field on a compact Riemannian manifold is Killing. Then, we find several necessary and sufficient conditions for a Jacobi-type vector field to be a Killing vector field on non-compact Riemannian manifolds. Further, we derive some characterizations of Euclidean spaces in terms of Jacobi-type vector fields. Finally, we provide examples of Jacobi-type vector fields on non-compact Riemannian manifolds, which are non-Killing.

scholarly journals H-CONTACT UNIT TANGENT SPHERE BUNDLES OF FOUR-DIMENSIONAL RIEMANNIAN MANIFOLDS

2011 ◽  
Vol 91 (2) ◽  
pp. 243-256 ◽  
Author(s):  
SUN HYANG CHUN ◽  
JEONGHYEONG PARK ◽  
KOUEI SEKIGAWA
Keyword(s):  
Sphere Bundle ◽  
Base Manifold ◽  
Tangent Sphere Bundle ◽  
Tangent Sphere ◽  
Contact Metric Structure ◽  
Standard Contact ◽  
Unit Tangent Sphere Bundles ◽  
Contact Unit ◽  
Necessary And Sufficient ◽  
Unit Tangent Sphere Bundle

AbstractWe study the geometric properties of a base manifold whose unit tangent sphere bundle, equipped with the standard contact metric structure, is H-contact. We prove that a necessary and sufficient condition for the unit tangent sphere bundle of a four-dimensional Riemannian manifold to be H-contact is that the base manifold is 2-stein.

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