Abstract
We show that every symplectic manifold of dimension ≥ 4 admits a complete compatible almost Kähler metric of negative scalar curvature. And we discuss the C 0-closure of the set of almost Kähler metrics of negative scalar curvature. Some local versions are also proved.
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Fintushel R., Stern R.J.: Knots, links, and 4-manifolds. Invent. Math. 134(2), 363–400 (1998)
Gompf, R.E., Stipsicz, A.I.: 4-Manifolds and Kirby calculus. Graduate Studies in Math., vol. 20. American Math. Soc. (1999)
Kang Y., Kim J.: Almost Kähler metrics with non-positive scalar curvature which are Euclidean away from a compact set. J. Korean Math. Soc. 41(5), 809–820 (2004)
Kim J.: A closed symplectic four-manifold has Almost Kähler metrics of negative scalar curvature. Ann. Global Anal. Geom. 33(2), 115–136 (2008)
Lohkamp J.: Metrics of negative Ricci curvature. Ann. Math. 140(2), 655–683 (1994)
Lohkamp J.: Curvature h-principles. Ann. Math. 142(2), 457–498 (1995)
Lohkamp J.: The space of negative scalar curvature metrics. Invent. Math. 110(2), 403–407 (1992)
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J. Kim was supported by the Korea Research Foundation grant funded by the Korean Government (MOEHRD) (R14-2002-044-01002-0).
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Kim, J. Almost Kähler metrics of negative scalar curvature on symplectic manifolds. Math. Z. 262, 381–388 (2009). https://doi.org/10.1007/s00209-008-0379-5
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DOI: https://doi.org/10.1007/s00209-008-0379-5