Kaluza–Klein type Ricci solitons on unit tangent sphere bundles

2018 ◽  
Vol 59 ◽  
pp. 184-203
Author(s):  
M.T.K. Abbassi ◽  
N. Amri ◽  
G. Calvaruso
Keyword(s):  
Ricci Solitons ◽  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles ◽  
Kaluza Klein

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.

On Einstein Riemannian g-natural metrics on unit tangent sphere bundles

2010 ◽  
Vol 38 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Oldřich Kowalski
Keyword(s):  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles

g-Natural Contact Metrics on Unit Tangent Sphere Bundles

2006 ◽  
Vol 151 (2) ◽  
pp. 89-109 ◽  
Author(s):  
M. T. K. Abbassi ◽  
G. Calvaruso
Keyword(s):  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles

scholarly journals PSEUDO-SYMMETRY ON UNIT TANGENT SPHERE BUNDLES

2016 ◽  
Vol 38 (2) ◽  
pp. 375-384
Author(s):  
Jong Taek Cho ◽  
Sun Hyang Chun
Keyword(s):  
Tangent Sphere ◽  
Unit Tangent Sphere Bundles

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
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