Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Harmonic two-forms in four dimensions


Author: Walter Seaman
Journal: Proc. Amer. Math. Soc. 112 (1991), 545-548
MSC: Primary 58G25; Secondary 53C20, 57N13
DOI: https://doi.org/10.1090/S0002-9939-1991-1062836-0
MathSciNet review: 1062836
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Conformal invariance of middle-dimensional harmonic forms is used to improve Kato's inequality for four-manifolds. An application to positively curved four-manifolds is given.


References [Enhancements On Off] (What's this?)

  • [1] P. Bérard, Spectral geometry: Direct and inverse problems (with an appendix by G. Besson), Lecture Notes in Math., vol. 1207, Springer-Verlag, 1986. MR 861271 (88f:58146)
  • [2] M. Berger, Sur les variétés $ \tfrac{4}{{23}}$-pincées de dimension 5, C. R. Acad. Sci. Paris Sér. I Math. 257 (1963). MR 0158332 (28:1557)
  • [3] A. Besse, Einstein manifolds, Ergeb. Math. Grenzgeb. (3), Folge, Band 10, Springer-Verlag, 1987. MR 867684 (88f:53087)
  • [4] J. P. Bourguignon, La conjecture de Hopf sur $ {\mathbb{S}^2} \times {\mathbb{S}^2}$, Géometrie riemannienne en dimension 4, Séminaire Arthur Besse, CEDIC Paris, 1981, pp. 347-355. MR 769145
  • [5] W. Seaman, Two forms on four manifolds, Proc. Amer. Math. Soc. 101 (1987), 353-357. MR 902555 (88h:53039)
  • [6] -, A pinching theorem for four manifolds, Geom. Dedicata 31 (1989), 37-40. MR 1009881 (90h:53043)
  • [7] M. Ville, Les variétés Riemanniennes de dimension $ 4\tfrac{4}{{19}}$-pinceés, Ann. Inst. Fourier (Grenoble) 39 (1989), 149-154. MR 1011981 (90f:53082)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G25, 53C20, 57N13

Retrieve articles in all journals with MSC: 58G25, 53C20, 57N13


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1062836-0
Keywords: Harmonic forms, Weitzenbock operator, curvature, four-manifolds
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society