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Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature

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Abstract

In this paper, we show several vanishing theorems for harmonic p-forms on compact manifolds, and \(L^q\) harmonic p-forms on complete noncompact manifolds with nonnegative scalar curvature, under various pointwise or integral curvature conditions. These conditions involve the positive Yamabe invariant, the weighted Poincaré inequality and the pure curvature tensor.

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Authors and Affiliations

  1. College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou, 350108, China

    Hezi Lin

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  1. Hezi Lin
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Correspondence to Hezi Lin.

Additional information

Supported by NSFC Grant No. 11831005, the Natural Science Foundation of Fujian Province, China (Grant No. 2017J01398).

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Lin, H. Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature. Geom Dedicata 201, 187–201 (2019). https://doi.org/10.1007/s10711-018-0388-4

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  • DOI: https://doi.org/10.1007/s10711-018-0388-4

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