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Complete minimal submanifolds of compact Lie groups

Abstract

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then employ our method to construct many examples of compact minimal submanifolds of the special unitary groups.

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Author information

Correspondence to Sigmundur Gudmundsson.

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Gudmundsson, S., Svensson, M. & Ville, M. Complete minimal submanifolds of compact Lie groups. Math. Z. 282, 993–1005 (2016). https://doi.org/10.1007/s00209-015-1574-9

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Keywords

  • Harmonic morphisms
  • Minimal submanifolds
  • Lie groups

Mathematics Subject Classification

  • 58E20
  • 53C43
  • 53C12