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논문KCI 등재

RICCI CURVATURE AND MONOPOLE CLASSES ON 3-MANIFOLDS

Chanyoung Sung
대한수학회 (The Korean Mathematical Society)|2012.09|대한수학회지 (Journal of the KMS)|제49권 제5호|pp. 965-976

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참고문헌

키워드

Ricci curvatureSeiberg-Witten equationsmonopole class
주제분류수학

초록

We prove an L2-estimate of Ricci curvature in terms of har-monic 1-forms on a closed oriented Riemannian 3-manifold admitting a solution of any rescaled Seiberg-Witten equations. We also give a neces-sary condition to be a monopole class on some special connected sums.

Abstract

We prove an L2-estimate of Ricci curvature in terms of har-monic 1-forms on a closed oriented Riemannian 3-manifold admitting a solution of any rescaled Seiberg-Witten equations. We also give a neces-sary condition to be a monopole class on some special connected sums.

참고문헌 (22)

  1. S. Bauer, "A stable cohomotopy re nement of Seiberg-Witten invariants. II", Invent. Math, 155(1), pp.21~40 (2004)
  2. S. Bauer, "A stable cohomotopy re nement of Seiberg-Witten invariants. I", Invent. Math, 155(1), pp.1~19 (2004)
  3. G. Besson, "Volume et entropie minimale des espaces locale- ment symetriques", Invent. Math, 103(2), pp.417~445 (1991)
  4. H.-D. Cao, "Equivariant cohomology and wall crossing formula in Seiberg- Witten theory", Math. Res. Lett, 5(6), pp.711~721 (1998)
  5. M. Gromov, "The classification of simply connected manifolds of positive scalar curvature", Ann. of Math, 111(3), pp.423~434 (1980)
  6. M. Gursky, "Four-manifolds with ffiW+ = 0 and Einstein constants of the sphere", Math. Ann, 318(3), pp.417~431 (2000)
  7. P. B. Kronheimer, "The genus of embedded surfaces in the projective plane", Math. Res. Lett, 1(6), pp.797~808 (1994)
  8. H. B. Lawson, "Spin Geometry" (1989), Princeton University Press
  9. C. LeBrun, "Four-manifolds without Einstein metric", Math. Res. Lett, 3(2), pp.133~147 (1996)
  10. C. LeBrun, "Yamabe constants and the perturbed Seiberg-Witten equations", Comm. Anal. Geom, 5(3), pp.535~553 (1997)
  11. C. LeBrun, "Curvature and smooth topology in dimension four, Global analysis and har- monic analysis", Semin. Congr, pp.179~200 (2000), Soc. Math
  12. C. LeBrun, "Ricci curvature, minimal volumes, and Seiberg-Witten theory", Invent. Math, 145(2), pp.279~316 (2001)
  13. C. LeBrun, "Einstein metrics, four-manifolds, and differential topology, Surveys in differen- tial geometry, Vol. VIII", pp.235~255 (2003), Int. Press
  14. J. Lee, "The Yamabe problem", Bull. Amer. Math. Soc, 17(1), pp.37~91 (1987)
  15. T. J. Li, "General wall crossing formula", Math. Res. Lett, 2(6), pp.797~810 (1995)
  16. J. Morgan, "The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifold" (1996), Princeton University Press
  17. C. Sung, "Surgery, curvature, and minimal volume", Ann. Global Anal. Geom, 26(3), pp.209~229 (2004)
  18. C. Sung, "Surgery and equivariant Yamabe invariant", Differential Geom. Appl, 24(3), pp.271~287 (2006)
  19. C. Sung, "Collapsing and monopole classes of 3-manifolds", J. Geom. Phys, 57(2), pp.549~559 (2007)
  20. C. Sung, "Surgery, Yamabe invariant, and Seiberg-Witten theory", J. Geom. Phys, 59(2), pp.246~255 (2009)
  21. C. Sung, "Finite group actions and G-monopole classes on smooth 4-manifolds", ~
  22. C. H. Taubes, "The Seiberg-Witten invariants and symplectic forms", Math. Res. Lett, 1(6), pp.809~822 (1994)

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