CONFORMAL COMPACTIFICATION OA ASYMPTOTICALLY EUCLIDEAN SCALAR-FLAT KAHLER SURFACES

  • Published : 1997.11.01

Abstract

We show that an asymptotically Euclidean scalar-flat Kahler metric ona complex surface can be smoothly conformally compactified at the infinity point. We discuss some implication of this, characterizing such metrics on $C^2$ blown up at some points.

Keywords

References

  1. Proc. Symp. Pure Math. A. M. S. v.54 Degeneration of Metrics with Bounded Curvature and Applications to Critical Metrics of Riemannian Functionals Anderson, M.
  2. Inventiones Math. v.102 Convergence and Rigidity of manifolds under Ricci Curvature Bounds Anderson, M.
  3. Proc. R. Soc. Lond. Ser. A v.372 Self-duality in four dimensional riemannian geometry Atiyah, M. F.;Hitchin, N. J.;Singer, I.M.
  4. Enistein Manifolds Besse, A.
  5. Kahler Einstein Metrics and Integral Invariants Futaki, A.
  6. Physics Letters v.78B Gravitational Muti-Instantons Gibbons, G. W.;Hawking, S. W.
  7. On Asymptotically Euclidean Scalar-Flat Kahler Surfaces Kim, J.
  8. General Relativity and Grav. v.17 Conformal Einstein spaces Kozameh, C. N.;Newman, E. T.;Tdo, K. P.
  9. Journal of Differential Geometry v.29 A Torelli Type Theorem for HyperKahler Metrics Kronheimer, P
  10. J. Am. Math. Soc. v.5 Kahler manifolds and bimeromorphic geometry I LeBrun, C.
  11. Journal of Differential Geometry v.34 Explicit self-dual metrics on$CP^2#...#CP^2$ LeBrun, C.
  12. Comm. Math. Physics v.118 Counterexamples to the Generalized Positive Action Conjecture LeBrun, C.
  13. Inv. Math. v.112 Existence and deformation theory for scalar flat Kahler metrics on compact complex surfaces LeBrun. C.
  14. Lecture Notes in Pure and Appl. Math. 143 Li, P;Yau,S. T.
  15. Multiple Integrals in the Calculus of Variations Morrey, C. B.
  16. Spinors and Space-time Penrose, R.;Rindler, W.
  17. Mathematische Annalen v.291 Algebraic Demension of Twistor Spaces and Scalar Curvature of Anti-Self-Dual Metrics Pontecorvo, M.
  18. J. Differential Geom. v.24 Compact self-dual manifolds with positive scalar curvature Poon, Y. S.