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Riemannian manifolds with harmonic curvature

Part of the Lecture Notes in Mathematics book series (LNM,volume 1156)

Keywords

  • Riemannian Manifold
  • Compact Manifold
  • Weyl Tensor
  • Compact Surface
  • Compact Riemannian Manifold

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References

  1. Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. 36, 235–249 (1957) (Zbl. 84.304)

    MathSciNet  MATH  Google Scholar 

  2. Atiyah, M.F., Hitchin, N.J., Singer, I.M.: Self-duality in four-dimensional Riemannian geometry. Proc. Roy. Soc. London A362, 425–461 (1978) (Zbl. 389.53011)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Berger, M.S.: Nonlinearity and Functional Analysis, Academic Press, 1977 (Zbl.368.47001)

    Google Scholar 

  4. Berger, M., Ebin, D.: Some decompositions of the space of symmetric tensors on a Riemannian manifold. J. Differential Geometry 3, 379–392 (1969) (Zbl. 194,531)

    MathSciNet  MATH  Google Scholar 

  5. Besse, A.L.: Einstein Manifolds (to appear)

    Google Scholar 

  6. Bourguignon, J.P.: Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein. Invent. Math. 63, 263–286 (1981) (Zbl. 456.53033)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Bourguignon, J.P.: Metrics with harmonic curvature. Global Riemannian Geometry (edited by T.J. Willmore and N.J. Hitchin), 18–26. Ellis Horwood, 1984

    Google Scholar 

  8. Bourguignon, J.P., Lawson, H.B.,Jr.: Yang-Mills theory: Its physical origins and differential geometric aspects. Seminar on Differential Geometry (edited by S.T. Yau), Ann. of Math. Studies No. 102, 395–421 (1982) (Zbl. 482.58007)

    Google Scholar 

  9. Derdziński, A.: On compact Riemannian manifolds with harmonic curvature. Math. Ann. 259, 145–152 (1982) (Zbl. 489.53042)

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Derdziński, A.: Self-dual Kähler manifolds and Einstein manifolds of dimension four. Compos. Math. 49, 405–433 (1983) (Zbl. 527.53030)

    MATH  Google Scholar 

  11. Derdziński, A.: Preliminary notes on compact four-dimensional Riemannian manifolds with harmonic curvature, 1983 (unpublished)

    Google Scholar 

  12. Derdziński, A.: An easy construction of new compact Riemannian manifolds with harmonic curvature (preliminary report). SFB/MPI 83–21, Bonn (1983)

    Google Scholar 

  13. Derdziński, A., Shen, C.L.: Codzzi tensor fields, curvature and Pontryagin forms. Proc. London Math. Soc. 47, 15–26 (1983) (Zbl. 519.53015)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. DeTurck, D.: private communication

    Google Scholar 

  15. Ebin, D.G.: The manifold of Riemannian metrics. Proc. of Symposia in Pure Math. 15, 11–40 (1970) (Zbl. 205,537) (Zbl. 135,225)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Hicks, N.: Linear perturbations of connexions. Michigan Math. J. 12, 389–397 (1965)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Lafontaine, J.: Remarques sur les variétés conformément plates. Math. Ann. 259, 313–319 (1982) (Zbl. 469.53036)

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. Matsushima, Y.: Remarks on Kähler-Einstein manifolds. Nagoya Math. J. 46, 161–173 (1972) (Zb. 249.53050)

    MathSciNet  MATH  Google Scholar 

  19. Roter, W.: private communication

    Google Scholar 

  20. Schouten, J.A.: Ricci Calculus. Springer-Verlag, 1954

    Google Scholar 

  21. Tanno, S.: Curvature tensors and covariant derivatives. Ann. Mat. Pura Appl. 96, 233–241 (1973) (Zbl. 277.53013)

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. Thorpe, J.: Some remarks on the Gauss-Bonnet integral. J. of Math. Mech. 18 779–786 (1969) (Zbl. 183,505)

    MathSciNet  MATH  Google Scholar 

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© 1985 Springer-Verlag

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Drdziński, A. (1985). Riemannian manifolds with harmonic curvature. In: Ferus, D., Gardner, R.B., Helgason, S., Simon, U. (eds) Global Differential Geometry and Global Analysis 1984. Lecture Notes in Mathematics, vol 1156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075087

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  • DOI: https://doi.org/10.1007/BFb0075087

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  • Print ISBN: 978-3-540-15994-0

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