Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 567993
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53B35

Retrieve articles in all journals with MSC: 53B35

Additional Information

Keywords: Sectional curvature, algebraic curvature tensor, Kähler curvture operator
Article copyright: © Copyright 1980 American Mathematical Society