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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.20 No.3

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A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄAHLER METRICS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.3, pp.199-206
https://doi.org/10.7468/jksmeb.2013.20.3.199
Kim, Jongsu
Kim,, J. (2013). A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄAHLER METRICS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(3), 199-206, https://doi.org/10.7468/jksmeb.2013.20.3.199

Abstract

We present a 4-dimensional nil-manifold as the first example of a closed non-K<TEX>$\ddot{a}$</TEX>hlerian symplectic manifold with the following property: a function is the scalar curvature of some almost K<TEX>$\ddot{a}$</TEX>hler metric iff it is negative somewhere. This is motivated by the Kazdan-Warner's work on classifying smooth closed manifolds according to the possible scalar curvature functions.

keywords
almost K<tex> $\ddot{a}$</tex>hler metric, scalar curvature, symplectic manifold

Reference

1.

Einstein manifolds. Ergebnisse der Mathematik, 3 Folge, Band 10.

2.

(1983). On the set of metrics associated to a symplectic or contact form. Bull. Institute of Math. Academia Sinica, 11, 297-308.

3.

4-Manifolds and Kirby Calculus. Graduate Studies in Math. v.20.

4.

(1985). Pseudoholomorphic curves in symplectic manifolds. Invent. Math., 82, 307-347. 10.1007/BF01388806.

5.

(1980). Spin and scalar curvature in the presence of a fundamental group. I. Ann. of Math., 111(2), 209-230. 10.2307/1971198.

6.

(1975). Existence and conformal deformation of metrics with prescribed gaussian and scalar curvatures. Ann. of Math., 101(2), 317-331. 10.2307/1970993.

7.

(2002). Deformation of almost Kahler metrics with constant scalar curvature on compact Kahler manifolds. Ann. Global. Anal. and Geom., 22, 49-73. 10.1023/A:1016217414800.

8.

Introduction to Symplectic Topology.

9.

(1984). Conformal deformation of a Riemannian metric to constant scalar curvature. J. Diff. Geom., 20, 479-495.

10.

(1984). An example of an almost Kahler manifold which is not Kahlerian. Boll. Un. Mat. Ital. A, 3(6), 383-392.

11.

Some nonlinear problems in Riemannian geometry.

12.

(1974). On compact four-dimensional Einstein manifolds. J. Diff. Geom., 9, 435-442.

13.

(1976). Some simple examples of symplectic manifolds. Proc. Amer. Math. Soc., 55, 467-468.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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