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New Bochner type theorems

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A classical theorem of Bochner asserts that the isometry group of a compact Riemannian manifold with negative Ricci curvature is finite. In this paper we give several extensions of Bochner’s theorem by allowing “small” positive Ricci curvature.

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Acknowledgements

Xiaoyang Chen is partially supported by National Natural Science Foundation of China no. 12171364. He thanks Prof. Binglong Chen and Prof. Botong Wang for helpful discussions. Fei Han is partially supported by the grant AcRF R-146-000-263-114 from National University of Singapore. He is indebted to Prof. Kefeng Liu and Prof. Weiping Zhang for helpful discussions. Both authors would like to thank the Mathematical Science Research Center at Chongqing University of Technology for hospitality during their visit and thank Prof. Wilderich Tuschmann for the helpful discussion.

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  1. School of Mathematical Sciences, Institute for Advanced Study, Tongji University, Shanghai, China

    Xiaoyang Chen

  2. Department of Mathematics, National University of Singapore, Singapore, Singapore

    Fei Han

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  1. Xiaoyang Chen
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  2. Fei Han
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Correspondence to Xiaoyang Chen.

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Chen, X., Han, F. New Bochner type theorems. Math. Ann. 388, 3757–3783 (2024). https://doi.org/10.1007/s00208-023-02612-y

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