Mathematische Zeitschrift

, Volume 281, Issue 3–4, pp 673–687 | Cite as

Extremal K-contact metrics

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Abstract

Extending a result of He to the non-integrable case of K-contact manifolds, it is shown that the transverse Hermitian scalar curvature may be interpreted as a moment map for the strict contactomorphism group. As a consequence, we may generalize the Sasaki–Futaki invariant to K-contact geometry and establish a number of elementary properties. Moreover, we prove that in dimension 5 certain deformation-theoretic results can be established also under weaker integrability conditions by exploiting the relationship between J-anti-invariant and self-dual 2-forms.

Keywords

Moment map K-Contact structure Extremal metrics Futaki-invariant 

Mathematics Subject Classification

53D10 53B35 53D20 
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Notes

Acknowledgments

The first named author is very grateful to Christina Tønnesen-Friedman and Charles Boyer for useful discussions. The first named author is also grateful to Vestislav Apostolov for helpful comments. Both authors are thankful to Joel Fine and Weiyong He for several useful discussions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Institut für Mathematik, Universität AugsburgUniversitätsstrasse 14AugsburgGermany

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