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Asymptotic behaviour of instantons on cylinder manifolds

  • Teng HuangEmail author
Article
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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., PQ 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., PQ 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.

Mathematics Subject Classification

58E15 81T13 

Notes

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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  2. 2. School of ScienceNantong UniversityNantongPeople’s Republic of China

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