Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ALMOST KAHLER METRICS WITH NON-POSITIVE SCALAR CURVATURE WHICH ARE EUCLIDEAN AWAY FROM A COMPACT SET

  • Published : 2004.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

On $R^{2n}$, n$\geq$2, with the standard symplectic structure we construct compatible almost K hler metrics with negative scalar curvature on a polydisc which are Euclidean away from the polydisc.c.

Keywords

References

  1. A. L. Besse, Einstein manifolds, Ergeb. Math. Grenzgeb. (3) Folge, Band 10, Springer-Verlag, 1987
  2. D. E. Blair, On the set of metrics associated to a symplectic or contact form, Inst. Math. Acad. Sinica 11 (1983), no. 3, 297-308
  3. M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307-347 https://doi.org/10.1007/BF01388806
  4. J. Lohkamp, Scalar curvature and hammocks, Math. Ann. 313 (1999), no. 3, 385-407 https://doi.org/10.1007/s002080050266
  5. J. Lohkamp, Metrics of negative Ricci curvature, Ann. of Math. 140 (1994), no. 3, 655-683 https://doi.org/10.2307/2118620
  6. C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994), 809-822 https://doi.org/10.4310/MRL.1994.v1.n6.a15

Cited by

  1. A closed symplectic four-manifold has almost Kähler metrics of negative scalar curvature vol.33, pp.2, 2008, https://doi.org/10.1007/s10455-007-9074-8
  2. MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE IN 3 DIMENSION vol.49, pp.3, 2012, https://doi.org/10.4134/BKMS.2012.49.3.581
  3. A NOTE ON DECREASING SCALAR CURVATURE FROM FLAT METRICS vol.35, pp.4, 2013, https://doi.org/10.5831/HMJ.2013.35.4.647
  4. Almost Kähler metrics of negative scalar curvature on symplectic manifolds vol.262, pp.2, 2009, https://doi.org/10.1007/s00209-008-0379-5
  5. MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1087