scholarly journals SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE

2008 ◽  
Vol 23 (4) ◽  
pp. 587-595 ◽  
Author(s):  
Seung-Su Hwang
2012 ◽  
Vol 49 (3) ◽  
pp. 655-667 ◽  
Author(s):  
Jeong-Wook Chang ◽  
Seung-Su Hwang ◽  
Gab-Jin Yun

1992 ◽  
Vol 35 (4) ◽  
pp. 455-462 ◽  
Author(s):  
D. E. Blair ◽  
D. Perrone

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.


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