A SIMPLY CONNECTED MANIFOLD WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES WITH DISTINCT SIGNS OF SCALAR CURVATURES

Title & Authors
A SIMPLY CONNECTED MANIFOLD WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES WITH DISTINCT SIGNS OF SCALAR CURVATURES
Kim, Jongsu;

Abstract
We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[$\small{{\omega}_i}$]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K$\small{\ddot{a}}$hler metrics in [5], satisfies $\small{Z(M,[[{\omega}_1]])={\infty}}$ and $\small{Z(M,[[{\omega}_2]])}$ < 0.
Keywords
almost K$\small{\ddot{a}}$hler metric;scalar curvature;symplectic manifold;symplectic deformation equivalence class;
Language
English
Cited by
1.
SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES,;

한국수학교육학회지시리즈B:순수및응용수학, 2015. vol.22. 4, pp.359-364
1.
SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES, The Pure and Applied Mathematics, 2015, 22, 4, 359
References
1.
R. Barlow, A simply connected surface of general type with $p_g$ = 0, Invent. Math. 79 (1985), no. 2, 293-301.

2.
A. L. Besse, Einstein Manifolds, Ergebnisse der Mathematik, 3 Folge, Band 10, Springer- Verlag, 1987.

3.
D. E. Blair, On the set of metrics associated to a symplectic or contact form, Bull. Inst. Math. Acad. Sinica 11 (1983), no. 3, 297-308.

4.
F. Catanese and C. LeBrun, On the scalar curvature of Einstein manifolds, Math. Res. Lett. 4 (1997), no. 6, 843-854.

5.
J. Kim and C. Sung, Scalar curvature functions of almost-Kahler metrics, http://arxiv.org/abs/1409.4004.

6.
D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford University Press, New York, 1998.

7.
C. T. McMullen and C. H. Taubes, 4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations, Math. Res. Lett. 6 (1999), no. 5-6, 681-696.

8.
J. Petean, The Yamabe invariant of simply connected manifolds, J. Reine Angew. Math. 523 (2006), 225-231.

9.
Y. Ruan, Symplectic topology on algebraic 3-folds, J. Differential Geom. 39 (1994), no. 1, 215-227.

10.
D. Salamon, Uniqueness of symplectic structures, Acta Math. Vietnam. 38 (2013), no. 1, 123-144.