sphere bundle
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2019 ◽  
Vol 6 (1) ◽  
pp. 279-293 ◽  
Author(s):  
Jong Taek Cho

AbstractFor a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(𝔿n+1) of a hyperbolic space 𝔿n+1 of constant curvature −1.


Author(s):  
Jorg Portegies ◽  
Stephan Meesters ◽  
Pauly Ossenblok ◽  
Andrea Fuster ◽  
Luc Florack ◽  
...  

2018 ◽  
Vol 10 (1) ◽  
pp. 152-166
Author(s):  
Esmaeil Peyghan ◽  
Farshad Firuzi

Abstract In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with respect to which the unit tangent sphere bundle with induced g-natural metric is totally geodesic. Also, we equip the unit tangent sphere bundle T1M with g-natural contact (paracontact) metric structures, and we show that such structures are totally geodesic K-contact (K-paracontact) submanifolds of TM, if and only if the base manifold (M, g) has positive (negative) constant sectional curvature. Moreover, we establish a condition for g-natural almost contact B-metric structures on T1Msuch that these structures be totally geodesic submanifolds of TM.


2018 ◽  
Vol 18 (1) ◽  
pp. 101-104 ◽  
Author(s):  
B. Bidabad ◽  
M. Yar Ahmadi

AbstractIn this paper we study an extension of Yamabe solitons for inequalities. We show that a Riemannian complete non-compact shrinking Yamabe soliton (M,g,V,λ) has finite fundamental group, provided that the scalar curvature is strictly bounded above byλ. Furthermore, an instance of illustrating the sharpness of this inequality is given. We also mention that the fundamental group of the sphere bundleSMis finite.


2017 ◽  
Vol 6 (4) ◽  
pp. 315-327
Author(s):  
E. Peyghan ◽  
L. Nourmohammadifar ◽  
A. Tayebi
Keyword(s):  

2013 ◽  
Vol 10 (09) ◽  
pp. 1320015 ◽  
Author(s):  
E. PEYGHAN ◽  
A. NADERIFARD ◽  
A. TAYEBI

Using the almost product structure given by Druta, we introduce a metrical framed f(3, -1)-structure on the tangent bundle of a Riemannian manifold. Then by restricting this metrical framed f(3, -1)-structure to the tangent sphere bundle, we obtain an almost metrical paracontact structure on the tangent sphere bundle.


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