Extremal K-contact metrics

Markus Upmeier, Mehdi Lejmi

Research output: Contribution to journalArticlepeer-review


Extending a result of He to the non-integrable case of K-contact manifolds, it is shown that 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.
Original languageEnglish
Pages (from-to)673-687
Number of pages14
JournalMathematische Zeitschrift
Issue number3
Publication statusPublished - 2015

Bibliographical note

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.


Dive into the research topics of 'Extremal K-contact metrics'. Together they form a unique fingerprint.

Cite this