JOURNAL BROWSE
Search
Advanced SearchSearch Tips
LOCALLY HOMOGENEOUS CRITICAL METRICS ON FOUR-DIMENSIONAL MANIFOLDS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
LOCALLY HOMOGENEOUS CRITICAL METRICS ON FOUR-DIMENSIONAL MANIFOLDS
Kang, Yu-Tae;
  PDF(new window)
 Abstract
We classify complete, locally homogeneous metrics with finite volume on four-dimensional manifolds which are critical points for the squared functionals of either the full Riemannian curvature tensor or the Weyl curvature tensor defined on the space of Riemannian metrics.
 Keywords
locally homogeneous metric;critical metric;-norm curvature functional;
 Language
English
 Cited by
1.
Critical metrics for quadratic functionals in the curvature on 4-dimensional manifolds, Differential Geometry and its Applications, 2011, 29, 5, 642  crossref(new windwow)
 References
1.
M. T. Anderson, Orbifold compactness for spaces of Riemannian metrics and applica- tions, Math. Ann. 331 (2005), no. 4, 739-778 crossref(new window)

2.
A. L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 10, Springer-Verlag, 1987

3.
A. Derdzinski, Self-dual Kahler manifolds and Einstein manifolds of dimension four, Compositio Math. 49 (1983), no. 3, 405-433

4.
R. O. Filipkiewicz, Four dimensional geometries, Ph. D. Thesis, University of Warwick, 1984

5.
G. R. Jensen, Homogeneous Einstein spaces of dimension four, J. Differential Geometry 3 (1969), 309-349

6.
J. Kim, Critical Kahler surfaces, Bull. Korean Math. Soc. 35 (1998), no. 3, 421-431

7.
F. Lamontagne, Une remarque sur la norme $L^2$ du tenseur de courbure, C. R. Acad. Sci. Paris Ser. I Math. 319 (1994), no. 3, 237-240

8.
F. Lamontagne, Critical metrics for the $L^2$ -norms of the curvature tensor, Ph. D. Thesis, 1993. Stony Brook

9.
C. LeBrun, Self-dual manifolds and hyperbolic geometry, Einstein metrics and Yang- Mills connections (Sanda, 1990), 99-131, Lecture Notes in Pure and Appl. Math., 145, Dekker, New York, 1993

10.
J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293-329 crossref(new window)

11.
M. S. Raghunathan, Discrete subgroups of Lie groups, Springer-Verlag, N.Y., Heider- berg, Berlin, 1972

12.
P. Scott, The geometries of 3-Manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401-487 crossref(new window)

13.
V. De Smedt and S. Salamon, Anti-self-dual metrics on Lie groups, Differential geometry and integrable systems (Tokyo, 2000), 63-75, Contemp. Math. 308, Amer. Math. Soc. Providence, RI, 2002

14.
W. P. Thurston, Three-Dimensional Geometry and Topology Vol. 1., Edited by Silvio Levy, Princeton Mathematical Series, 35, Princeton Univ. Press, Princeton, New Jersey, 1997

15.
G. Tian and J. Viaclovsky, Bach-flat asymptotically locally Euclidean metrics, Invent. Math. 160 (2005), no. 2, 357-415 crossref(new window)

16.
P. Bernat, N. Conze, M. Duflo, M. Levy-Nahas, M. Rais, P. Renouard, and M. Vergne, Representations des groupes de Lie resolubles, Monographies de la Societe Mathematique de France, No. 4. Dunod, Paris, 1972

17.
C. T. C. Wall, Geometries and geometric structures in real dimension 4 and complex dimension 2, Lecture Notes in Math., 1167, Springer, Berlin, 1985, 268-292 crossref(new window)

18.
C. T. C. Wall, Geometric structures on compact complex analytic surfaces, Topology 25 (1986), no. 2, 119-153 crossref(new window)