Korean J. Math. Vol. 21 No. 4 (2013) pp.473-481
DOI: https://doi.org/10.11568/kjm.2013.21.4.473

Scalar curvature functions of almost-K\"{a}hler metrics on a closed solv-manifold

Main Article Content

Yutae Kang
Jongsu Kim

Abstract

We discuss on the classification problem of symplectic manifolds into three families according to
the scalar curvature functions of almost K\"{a}hler metrics they admit. We also
present a 4-dimensional solv-manifold as an example which belongs to one of the three families.



Article Details

Supporting Agencies

the National Research Foundation of Korea(NRF) grant funded by the Korea government(MOE) (No. NRF-2010-0011704)

References

[1] L. Auslander, L. Green and F. Hahn, Flows on some three dimensional homo- geneous spaces, Bull. Amer. Math. Soc. 67 (1961), 494-497. Google Scholar

[2] A. L. Besse, Einstein manifolds. Ergebnisse der Mathematik, 3 Folge, Band 10, Springer-Verlag, 1987. Google Scholar

[3] D. E. Blair, On the set of metrics associated to a symplectic or contact form, Bull. Inst. Math. Acad. Sin. 11 (1983), 297-308. Google Scholar

[4] M. Fern andez and A. Gray, Compact symplectic solvmanifolds not admitting complex structures, Geom. Dedicata 34 (1990), 295-299. Google Scholar

[5] J.L. Kazdan and F.W. Warner, Existence and conformal deformation of metrics with prescribed gaussian and scalar curvatures, Ann. of Math. 101 (2) (1975), 317-331. Google Scholar

[6] J. Kim and C. Sung, Deformation of almost K ̈ahler metrics with constant scalar curvature on compact K ̈ahler manifolds, Ann. Global Anal. Geom. 22 (2002), 49-73. Google Scholar

[7] J. Kim, A Note On Scalar Curvature Functions of Almost-K ̈ahler Metrics, Jour. Korean Soc. Math. Edu. Ser. B, to appear. Google Scholar

[8] D. McDuff and D. Salamon: Introduction to Symplectic Topology, Oxford Uni- versity Press, New York 1998. Google Scholar