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Proceedings of the American Mathematical Society

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A curvature normal form for $ 4$-dimensional Kähler manifolds


Author: David L. Johnson
Journal: Proc. Amer. Math. Soc. 79 (1980), 462-464
MSC: Primary 53B35
DOI: https://doi.org/10.1090/S0002-9939-1980-0567993-0
MathSciNet review: 567993
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Abstract: A curvature operator R is said to possess a normal form relative to some space of curvature operators $ \mathcal{P}$ if R is determined uniquely in $ \mathcal{P}$ by the critical points and critical values of the associated sectional curvature function. It is shown that any curvature operator of Kähler type in real dimension 4 with positive-definite Ricci curvature has a normal form relative to the space of all Kähler operators.


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

  • [1] D. L. Johnson, A normal form for curvature, Ph.D. Thesis, M.I.T., 1977.
  • [2] David L. Johnson, Sectional curvature and curvature normal forms, Michigan Math. J. 27 (1980), no. 3, 275–294. MR 584692
  • [3] I. M. Singer and J. A. Thorpe, The curvature of 4-dimensional Einstein spaces, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 355–365. MR 0256303

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567993-0
Keywords: Sectional curvature, algebraic curvature tensor, Kähler curvture operator
Article copyright: © Copyright 1980 American Mathematical Society