A curvature normal form for $4$-dimensional Kähler manifolds
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- by David L. Johnson PDF
- Proc. Amer. Math. Soc. 79 (1980), 462-464 Request permission
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
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D. L. Johnson, A normal form for curvature, Ph.D. Thesis, M.I.T., 1977.
- David L. Johnson, Sectional curvature and curvature normal forms, Michigan Math. J. 27 (1980), no. 3, 275–294. MR 584692
- 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
Additional Information
- © Copyright 1980 American Mathematical Society
- 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