A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄAHLER METRICS

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Sogang University)

Kim, Jongsu. (2013). A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄHLER METRICS. 한국수학교육학회지시리즈B:순수및응용수학, 20(3), 199-206, https://doi.org/10.7468/jksmeb.2013.20.3.199

복사

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

참고문헌

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

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

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

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

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

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

(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.

Introduction to Symplectic Topology.

(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.

바로가기메뉴

논문 상세

Vol.20 No.3

A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄHLER METRICS

A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄAHLER METRICS

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학