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Ricci Deformation of the Metric on Riemannian Orbifolds

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Abstract

In this note we generalize the Huisken’s (J Diff Geom 21:47–62, 1985) result to Riemannian orbifolds. We show that on any n-dimensional (n ≥ 4) orbifold of positive scalar curvature the metric can be deformed into a metric of constant positive curvature, provided the norm of the Weyl conformal curvature tensor and the norm of the traceless Ricci tensor are not large compared to the scalar curvature at each point, and therefore generalize 3-orbifolds result proved by Hamilton [Three- orbifolds with positive Ricci curvature. In: Cao HD, Chow B, Chu SC, Yau ST (eds) Collected Papers on Ricci Flow, Internat. Press, Somerville, 2003] to n-orbifolds (n ≥ 4).

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  1. Department of Mathematics, East China Normal University, Dong Chuan Road 500, Shanghai, 200241, People’s Republic of China

    Jia-Yong Wu

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  1. Jia-Yong Wu
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Correspondence to Jia-Yong Wu.

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This work is partially supported by the NSFC10871069.

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Wu, JY. Ricci Deformation of the Metric on Riemannian Orbifolds. Results. Math. 57, 377–386 (2010). https://doi.org/10.1007/s00025-010-0036-2

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  • DOI: https://doi.org/10.1007/s00025-010-0036-2

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