scholarly journals On the Webster Scalar Curvature Problem on the CR Sphere with a Cylindrical-Type Symmetry

2012 ◽  
Vol 23 (4) ◽  
pp. 1674-1702 ◽  
Author(s):  
Daomin Cao ◽  
Shuangjie Peng ◽  
Shusen Yan
Keyword(s):  
Scalar Curvature ◽  
Type Symmetry ◽  
Webster Scalar Curvature ◽  
Curvature Problem

Topological tools for the prescribed scalar curvature problem on S n

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Dina Abuzaid ◽  
Randa Ben Mahmoud ◽  
Hichem Chtioui ◽  
Afef Rigane
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Standard Sphere ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Hopf Formula ◽  
Curvature Problem ◽  
Formula Type

AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

A Variational Characterization of Contact Metric Manifolds With Vanishing Torsion

1992 ◽  
Vol 35 (4) ◽  
pp. 455-462 ◽  
Author(s):  
D. E. Blair ◽  
D. Perrone
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Integral Functional ◽  
Riemannian Metrics ◽  
Contact Manifold ◽  
Contact Condition ◽  
Contact Metric Manifolds ◽  
Point Condition ◽  
Webster Scalar Curvature ◽  
Group Of Isometries

AbstractChern and Hamilton considered the integral of the Webster scalar curvature as a functional on the set of CR-structures on a compact 3-dimensional contact manifold. Critical points of this functional can be viewed as Riemannian metrics associated to the contact structure for which the characteristic vector field generates a 1-parameter group of isometries i.e. K-contact metrics. Tanno defined a higher dimensional generalization of the Webster scalar curvature, computed the critical point condition of the corresponding integral functional and found that it is not the K-contact condition. In this paper two other generalizations are given and the critical point conditions of the corresponding integral functionals are found. For the second of these, this is the K-contact condition, suggesting that it may be the proper generalization of the Webster scalar curvature.

Sign in / Sign up

Export Citation Format

Share Document