scholarly journals CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

2012 ◽  
Vol 49 (3) ◽  
pp. 655-667 ◽  
Author(s):  
Jeong-Wook Chang ◽  
Seung-Su Hwang ◽  
Gab-Jin Yun
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Total Scalar Curvature

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.

The Abbena-Thurston Manifold as a Critical Point

1996 ◽  
Vol 39 (3) ◽  
pp. 352-359 ◽  
Author(s):  
Joon-Sik Park ◽  
Won Tae Oh
Keyword(s):  
Scalar Curvature ◽  
Critical Point ◽  
Ricci Operator

AbstractThe Abbena-Thurston manifold (M,g) is a critical point of the functional where Q is the Ricci operator and R is the scalar curvature, and then the index of I(g) and also the index of — I(g) are positive at (M,g).

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