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Variational properties of quadratic curvature functionals

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Abstract

In this paper, we investigate a class of quadratic Riemannian curvature functionals on closed smooth manifold M of dimension n ⩾ 3 on the space of Riemannian metrics on M consisting of metrics with unit volume. We study the stability of these functionals at the metric with constant sectional curvature as its critical point.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11571304).

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Weimin Sheng & Lisheng Wang

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  1. Weimin Sheng
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  2. Lisheng Wang
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Correspondence to Weimin Sheng.

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Sheng, W., Wang, L. Variational properties of quadratic curvature functionals. Sci. China Math. 62, 1765–1778 (2019). https://doi.org/10.1007/s11425-017-9232-6

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  • DOI: https://doi.org/10.1007/s11425-017-9232-6

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