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Manifolds of positive Ricci curvature, quadratically asymptotically nonnegative curvature, and infinite Betti numbers

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Abstract

In a previous paper (Jiang and Yang (2021)), we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimensions greater than or equal to 6. The purpose of the present paper is to use a different technique to exhibit a family of complete I-dimensional (I ≽ 5) Riemannian manifolds of positive Ricci curvature, quadratically asymptotically nonnegative sectional curvature, and certain infinite Betti numbers bj (2 ≼ j ≼ I − 2).

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11571228 and 12071283) and a research fund of Shanghai Normal University (Grant No. SK202002).

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Authors and Affiliations

  1. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China

    Huihong Jiang

  2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yihu Yang

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  1. Huihong Jiang
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  2. Yihu Yang
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Correspondence to Yihu Yang.

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Jiang, H., Yang, Y. Manifolds of positive Ricci curvature, quadratically asymptotically nonnegative curvature, and infinite Betti numbers. Sci. China Math. 65, 2183–2200 (2022). https://doi.org/10.1007/s11425-021-1905-6

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  • DOI: https://doi.org/10.1007/s11425-021-1905-6

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