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A simply connected manifold with two symplectic deformation equivalence classes with distinct signs of scalar curvatures

김종수
대한수학회 (The Korean Mathematical Society)|2014.10|대한수학회논문집 (Communications of the KMS)|제29권 제4호|pp. 549-554

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참고문헌

키워드

scalar curvaturealmost K¨ahler metricsymplectic manifoldsymplectic deformation equivalence class
주제분류수학

초록

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[ω1]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K¨ahler metrics in [5], satisfies Z(M, [[ω1]]) = 1 and Z(M, [[ω2]]) < 0.

Abstract

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[ω1]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K¨ahler metrics in [5], satisfies Z(M, [[ω1]]) = 1 and Z(M, [[ω2]]) < 0.

참고문헌 (10)

  1. R. Barlow, "A simply connected surface of general type with pg = 0", Invent. Math, 79(2), pp.293~301 (1985)
  2. A. L. Besse, "Einstein Manifolds, Ergebnisse der Mathematik", 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(3), pp.297~308 (1983)
  4. F. Catanese, "On the scalar curvature of Einstein manifolds", Math. Res. Lett, 4(6), pp.843~854 (1997)
  5. "Scalar curvature functions of almost-Kahler metrics"[URL]
  6. D. McDuff, "Introduction to Symplectic Topology" (1998), Oxford University Press
  7. C. T. McMullen, "4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations", Math. Res. Lett, 6(5-6), pp.681~696 (1999)
  8. J. Petean, "The Yamabe invariant of simply connected manifolds", J. Reine Angew. Math, 523, pp.225~231 (2006)
  9. Y. Ruan, "Symplectic topology on algebraic 3-folds", J. Differential Geom, 39(1), pp.215~227 (1994)
  10. D. Salamon, "Uniqueness of symplectic structures", Acta Math. Vietnam, 38(1), pp.123~144 (2013)

관련 논문AI추천

SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES김종수한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제4호SCALAR CURVATURE FUNCTIONS OF ALMOST-K¨AHLER METRICS ON A CLOSED SOLV-MANIFOLD강유태, 김종수강원경기수학회 · 한국수학논문집2013 · 제21권 제4호A NOTE ON SCALAR CURVATURE FUNCTIONS OF ALMOST-KÄAHLER METRICS김종수한국수학교육학회 · 이론수학과 교직수학2013 · 제20권 제3호Anti-symplectic involutions on non-K\＂ ahler symplectic 4-manifolds조용승, 홍윤희대한수학회 · 대한수학회지2007 · 제44권 제4호LOCALLY CONFORMAL K¨AHLER MANIFOLDS AND CONFORMAL SCALAR CURVATURE김재만대한수학회 · 대한수학회논문집2010 · 제25권 제2호Harmonic K\＂{a}hler forms on hyperk\＂{a}hler manifolds박광순대한수학회 · 대한수학회논문집2003 · 제18권 제3호

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