A curvature normal form for -dimensional Kähler manifolds
Author: David L. Johnson
Journal: Proc. Amer. Math. Soc. 79 (1980), 462-464
MSC: Primary 53B35
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 if R is determined uniquely in 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.
-  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
- D. L. Johnson, A normal form for curvature, Ph.D. Thesis, M.I.T., 1977.
- -, Sectional curvature and curvature normal forms, Michigan Math. J. (to appear). MR 584692 (82g:53073)
- I. M. Singer and J. A. Thorpe, The curvature of 4-dimensional Einstein space, Global Analysis, Univ. of Tokyo Press, Tokyo, 1969, pp. 355-365. MR 0256303 (41:959)
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Keywords: Sectional curvature, algebraic curvature tensor, Kähler curvture operator
Article copyright: © Copyright 1980 American Mathematical Society