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Harmonic maps in Kähler geometry and deformation theory

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Harmonic Maps

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 949))

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Bibliography

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

    MathSciNet  MATH  Google Scholar 

  2. R. L. Bishop and S. I. Goldberg, "On the second cohomology group of a Kähler manifold of positive curvature," Proc. Amer. Math. Soc. 16 (1965), p.119–122.

    MathSciNet  MATH  Google Scholar 

  3. E. Calabi and E. Vesentini, "On compact locally symmetric Kahler manifolds," Ann. of Math. 71 (1960), p.472–507.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Douady, Le problème des modules pour les sous-espaces analytiques d'un espace analytique donné, Ann. Inst. Fourier (Grenoble) 16 (1966), p.1–95.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds," Amer. J. Math. 86 (1964), p.109–160.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Eells and J. C. Wood, "Restrictions on harmonic maps of surfaces," Topology 15 (1976), p.263–266.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Frankel, "Manifolds with positive curvature," Pacific J. Math. 11 (1961), p.165–174.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Grothendieck, "Sur la classification des fibres holomorphes sur la sphère de Riemann," Amer. J. Math. 79 (1957), p.121–138.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Kalka, "Deformation of submanifolds of strongly negatively curved manifolds," Math. Ann. 251 (1980), p.243–248.

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Kalka, B. Shiffman and B. Wong, "Finiteness and rigidity theorems for holomorphic mappings," to appear.

    Google Scholar 

  11. S. Kobayashi and T. Ochiai, "Characterizations of complex projective space and hyperquadrics," J. Math Kyoto Univ. 13 (1973), p.31–47.

    MathSciNet  MATH  Google Scholar 

  12. S. Kobayashi and J. Wu, "On holomorphic sections of certain hermitian vector bundles," Math. Ann. 189 (1970), p.1–4.

    Article  MathSciNet  MATH  Google Scholar 

  13. K. Kodaira and D. C. Spencer, "On deformations of complex analytic structures, III, Stability theorems," Ann. of Math. 71 (1960), p.43–76.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Kuranishi, "On locally complete families of complex analytic structures," Ann. of Math. 75 (1962), p.536–577.

    Article  MathSciNet  MATH  Google Scholar 

  15. T. Mabuchi, "ℂ-actions and algebraic threefolds with ample tangent bundle," Nagoya Math. J. 69 (1978), p.33–64.

    Article  MathSciNet  MATH  Google Scholar 

  16. G. D. Mostow, Strong Rigidity of Locally Symmetric Spaces, Ann. of Math. Studies 78 (1973), Princeton University Press.

    Google Scholar 

  17. J. Sacks and K. Uhlenbeck, "The existence of minimal immersions of 2-spheres", preprint.

    Google Scholar 

  18. J. H. Sampson, "Some properties and applications of harmonic mappings," Ann. Sci. École Norm. Sup. 11 (1978), p.211–228.

    MathSciNet  MATH  Google Scholar 

  19. Y. T. Siu, "The complex-analyticity of harmonic maps and the strong rigidity of compact Kahler manifolds," Ann. of Math. 112 (1980), p.73–111.

    Article  MathSciNet  MATH  Google Scholar 

  20. _____, "Some remarks on the complex analyticity of harmonic maps," preprint.

    Google Scholar 

  21. _____, "Curvature characterization of hyperquadrics," Duke Math. J. 47 (1980), 641–654.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tulane University, 70118, New Orleans, La.

    M. Kalka

Authors
  1. M. Kalka
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Editor information

Ronald J. Knill Morris Kalka Howard C. J. Sealey

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© 1982 Springer-Verlag

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Kalka, M. (1982). Harmonic maps in Kähler geometry and deformation theory. In: Knill, R.J., Kalka, M., Sealey, H.C.J. (eds) Harmonic Maps. Lecture Notes in Mathematics, vol 949. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069757

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  • DOI: https://doi.org/10.1007/BFb0069757

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11595-3

  • Online ISBN: 978-3-540-39360-3

  • eBook Packages: Springer Book Archive

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