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Asymptotic behaviour of instantons on cylinder manifolds

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Abstract

In this article, we study the instanton equation on the cylinder over a closed manifold X which admits non-zero smooth 3-form P and 4-form Q. Our results are (1) if X is a good manifold, i.e., P, Q satisfying \(d*_{X}P=d*_{X}Q=0\), then the instanton with integrable curvature decays exponentially at the ends, and, (2) if X is a real Killing spinor manifold, i.e., P, Q satisfying \(dP=4Q\) and \(d*_{X}Q=(n-3)*_{X}P\), we prove that the solution of instanton equation is trivial under some mild conditions.

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Acknowledgements

I would like to thank the anonymous referee for a careful reading of my manuscript and helpful comments. This work is supported by Nature Science Foundation of China No. 11801539 and Postdoctoral Science Foundation of China Nos. 2017M621998, 2018T110616.

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  1. Teng Huang

    Present address: School of Science, Nantong University, Nantong, Jiangsu, 226007, People’s Republic of China

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  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

    Teng Huang

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Huang, T. Asymptotic behaviour of instantons on cylinder manifolds. manuscripta math. 162, 171–189 (2020). https://doi.org/10.1007/s00229-019-01124-x

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