On Vanishing Theorems for Locally Conformally Flat Riemannian Manifolds with an Integral Pinching Condition

Duc Thoan Pham , Van Khien Tran , Thi Hong Nguyen

Communications in Mathematics and Statistics ›› : 1 -12.

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Communications in Mathematics and Statistics ›› : 1 -12. DOI: 10.1007/s40304-023-00372-4
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On Vanishing Theorems for Locally Conformally Flat Riemannian Manifolds with an Integral Pinching Condition

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Abstract

In this paper, we show some vanishing theorems for harmonic p-forms on a locally conformally flat Riemannian manifold. In the concrete, provided that the integral of the traceless Ricci tensor has a suitable bound, we obtain a vanishing theorem for them without any scalar curvature conditions. Another theorem is also given under the condition on nonpositive scalar curvature, which improves and extends the ones previous.

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Harmonic p-form / Vanishing theorem / Locally conformally flat Riemannian manifold

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Duc Thoan Pham,Van Khien Tran,Thi Hong Nguyen. On Vanishing Theorems for Locally Conformally Flat Riemannian Manifolds with an Integral Pinching Condition. Communications in Mathematics and Statistics 1-12 DOI:10.1007/s40304-023-00372-4

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