The zeroes of nonnegative holomorphic curvature operators
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- by A. M. Naveira and C. Fuertes
- Trans. Amer. Math. Soc. 210 (1975), 139-147
- DOI: https://doi.org/10.1090/S0002-9947-1975-0405274-9
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Abstract:
Here, we study the structure of points in a holomorphic Grassmann’s submanifold where the holomorphic sectional curvature assumes its minimum and maximum. For spaces of nonnegative holomorphic sectional curvature we study the set of points on which it assumes the value zero. We show that the minimum and maximum sets of holomorphic sectional curvature are the intersections of a holomorphic Grassmann’s submanifold with linear complex holomorphic subspaces of type (1, 1).References
- Robert B. Gardner, Some applications of the retraction theorem in exterior algebra, J. Differential Geometry 2 (1968), 25–31. MR 241458
- Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0238225
- Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
- John A. Thorpe, The zeros of nonnegative curvature operators, J. Differential Geometry 5 (1971), 113–125. MR 290285
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 210 (1975), 139-147
- MSC: Primary 53B35
- DOI: https://doi.org/10.1090/S0002-9947-1975-0405274-9
- MathSciNet review: 0405274