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Algebraic conditions for the positivity of sectional curvature

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Abstract

We examine algebraic conditions for the sectional positivity of the Riemann curvature operator. We describe sufficient conditions for dimension \(n=4\), and complete characterisation for a dense open subset of the space of operators in dimension 4. We briefly examine higher-dimensional curvature operators.

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Acknowledgements

I would like to thank my doctoral advisor Ioan Bucataru for guidance in writing this article, Renato Ghini Bettiol for his encouragement and interesting discussions on the topic, and the anonymous reviewer for their thoughtful reading of the work and many helpful suggestions.

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  1. Faculty of Mathematics, Alexandru Ioan Cuza University, Iaşi, Romania

    Dan Gregorian Fodor

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  1. Dan Gregorian Fodor
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Correspondence to Dan Gregorian Fodor.

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Fodor, D.G. Algebraic conditions for the positivity of sectional curvature. Beitr Algebra Geom 61, 283–295 (2020). https://doi.org/10.1007/s13366-019-00464-9

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  • DOI: https://doi.org/10.1007/s13366-019-00464-9

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