scholarly journals HOMOGENEOUS AND H-CONTACT UNIT TANGENT SPHERE BUNDLES

2010 ◽  
Vol 88 (3) ◽  
pp. 323-337 ◽  
Author(s):  
G. CALVARUSO ◽  
D. PERRONE
Keyword(s):  
Riemannian Manifolds ◽  
Einstein Manifolds ◽  
Tangent Sphere ◽  
Contact Metric Structure ◽  
Metric Structures ◽  
Standard Contact ◽  
Unit Tangent Sphere Bundles ◽  
Contact Unit ◽  
Two Parameter ◽  
Kaluza Klein

AbstractWe prove that all g-natural contact metric structures on a two-point homogeneous space are homogeneous contact. The converse is also proved for metrics of Kaluza–Klein type. We also show that if (M,g) is an Einstein manifold and $\tilde G$ is a Riemannian g-natural metric on T1M of Kaluza–Klein type, then $(T_1 M,\tilde \eta ,\tilde G)$ is H-contact if and only if (M,g) is 2-stein, so proving that the main result of Chun et al. [‘H-contact unit tangent sphere bundles of Einstein manifolds’, Q. J. Math., to appear. DOI: 10.1093/qmath/hap025] is invariant under a two-parameter deformation of the standard contact metric structure on T1M. Moreover, we completely characterize Riemannian manifolds admitting two distinct H-contact g-natural contact metric structures, with associated metric of Kaluza–Klein type.

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.

H-CONTACT UNIT TANGENT SPHERE BUNDLES OF EINSTEIN MANIFOLDS

2009 ◽  
Vol 62 (1) ◽  
pp. 59-69 ◽  
Author(s):  
S. H. Chun ◽  
J. H. Park ◽  
K. Sekigawa
Keyword(s):  
Einstein Manifolds ◽  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles ◽  
Contact Unit

scholarly journals A REMARK ON H-CONTACT UNIT TANGENT SPHERE BUNDLES

2011 ◽  
Vol 48 (2) ◽  
pp. 329-340 ◽  
Author(s):  
Sun-Hyang Chun ◽  
Hong-Kyung Pak ◽  
Jeong-Hyeong Park ◽  
Kouei Sekigawa
Keyword(s):  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles ◽  
Contact Unit

η-EINSTEIN TANGENT SPHERE BUNDLES OF CONSTANT RADII

2009 ◽  
Vol 06 (06) ◽  
pp. 965-984 ◽  
Author(s):  
SUN HYANG CHUN ◽  
JEONG HYEONG PARK ◽  
KOUEI SEKIGAWA
Keyword(s):  
Symmetric Space ◽  
Einstein Manifold ◽  
Sphere Bundle ◽  
Base Manifold ◽  
Tangent Sphere Bundle ◽  
3 Dimensional ◽  
Tangent Sphere ◽  
Locally Symmetric Space ◽  
Contact Metric Structure ◽  
Standard Contact

We study the geometric properties of the base manifold for the tangent sphere bundle of radius r satisfying the η-Einstein condition with the standard contact metric structure. One of the main theorems is that the tangent sphere bundle of the n(≥3)-dimensional locally symmetric space, equipped with the standard contact metric structure, is an η-Einstein manifold if and only if the base manifold is a space of constant sectional curvature [Formula: see text] or [Formula: see text].

scholarly journals $H$-Contact Unit Tangent Sphere Bundles

2007 ◽  
Vol 37 (5) ◽  
pp. 1435-1458 ◽  
Author(s):  
G. Calvaruso ◽  
D. Perrone
Keyword(s):  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles ◽  
Contact Unit

scholarly journals Bootstrap bounds on closed Einstein manifolds

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
James Bonifacio ◽  
Kurt Hinterbichler
Keyword(s):  
Compact Riemannian Manifold ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Einstein Manifolds ◽  
Consistency Conditions ◽  
Conformal Field ◽  
Geometric Data ◽  
Conformal Bootstrap ◽  
Laplacian Operators ◽  
Kaluza Klein

Abstract A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

scholarly journals Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 72
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri
Keyword(s):  
Gaussian Curvature ◽  
Tangent Bundle ◽  
Two Dimensional ◽  
Constant Gaussian Curvature ◽  
Metric Structures ◽  
Unit Tangent Bundle ◽  
Tangent Bundles ◽  
Full Classification ◽  
Kaluza Klein

In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

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