Extremal K-contact metrics

Markus Upmeier; Mehdi Lejmi

doi:10.1007/s00209-015-1503-y

Extremal K-contact metrics

Markus Upmeier, Mehdi Lejmi

Mathematical Science

City University of New York

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	673-687
Number of pages	14
Journal	Mathematische Zeitschrift
Volume	281
Issue number	3
DOIs	https://doi.org/10.1007/s00209-015-1503-y
Publication status	Published - 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.

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abstract = "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.",

author = "Markus Upmeier and Mehdi Lejmi",

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AU - Lejmi, Mehdi

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PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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DO - 10.1007/s00209-015-1503-y

M3 - Article

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SP - 673

EP - 687

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3

ER -

Extremal K-contact metrics

Abstract

Bibliographical note

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