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Archiv der Mathematik

, Volume 110, Issue 6, pp 629–635 | Cite as

A volume decreasing theorem for \(\mathbf{V}\)-harmonic maps and applications

  • Guangwen ZhaoEmail author
Article
  • 82 Downloads

Abstract

We establish a volume decreasing result for V-harmonic maps between Riemannian manifolds. We apply this result to obtain corresponding results for Weyl harmonic maps from conformal Weyl manifolds to Riemannian manifolds. We also obtain corresponding results for holomorphic maps from almost Hermitian manifolds to quasi-Kähler manifolds, which generalize or improve the partial results in Goldberg and Har’El (Bull Soc Math Grèce 18(1):141–148, 1977, J Differ Geom 14(1):67–80, 1979).

Keywords

Volume decreasing V-harmonic map Holomorphic map Almost Hermitian manifold 

Mathematics Subject Classification

58E20 32Q60 32H02 

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Notes

Acknowledgements

The author gratefully acknowledges the much helpful guidance of Professor Qun Chen.

References

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China

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