Abstract
In this paper, we first calculate for a Riemannian manifold the minimal norm tensor of the covariant derivative of the Ricci curvature. Then we show that, for an n-dimensional (\(n\geqslant 4\)) umbilic-free hypersurface of the space form, if the covariant derivative of the Ricci curvature has vanishing minimal norm tensor, it has parallel Ricci curvature or it is a special rotational hypersurface \(M^n_{c,\sigma }\).
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The authors would like to thank the referees for their helpful comments and suggestions.
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The first author is supported by the Grant No. 12161092 of the National Natural Science Foundation of China. The second author is supported by the Grant No. 12201554 of the National Natural Science Foundation of China and Yunnan Fundamental Research Projects (Grant No. LS21022).
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Guo, Z., Li, H. Hypersurfaces of the Space form for Which the Covariant Derivative of Their Ricci Tensors has Vanishing Minimal Norm Tensor. Results Math 79, 67 (2024). https://doi.org/10.1007/s00025-023-02085-0
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DOI: https://doi.org/10.1007/s00025-023-02085-0