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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The zeroes of nonnegative holomorphic curvature operators

Authors: A. M. Naveira and C. Fuertes
Journal: Trans. Amer. Math. Soc. 210 (1975), 139-147
MSC: Primary 53B35
MathSciNet review: 0405274
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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).

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Keywords: Decomposable holomorphic vectors, holomorphic curvature operators, holomorphic sectional curvatures
Article copyright: © Copyright 1975 American Mathematical Society