Asian Journal of Mathematics

Volume 17 (2013)

Number 2

Existence of compatible contact structures on $G_2$-manifolds

Pages: 321 – 334

DOI: https://dx.doi.org/10.4310/AJM.2013.v17.n2.a3

Authors

M. Firat Arikan (Department of Mathematics, University of Rochester, Rochester, New York, U.S.A.; Max Planck Institute for Mathematics, Bonn, Germany)

Hyunjoo Cho (Department of Mathematics, University of Rochester, Rochester, New York, U.S.A.)

Sema Salur (Department of Mathematics, University of Rochester, Rochester, New York, U.S.A.)

Abstract

In this paper, we show the existence of (co-oriented) contact structures on certain classes of $G_2$-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure (and so any manifold with $G_2$-structure) admits an almost contact structure. We also construct explicit almost contact metric structures on manifolds with $G_2$-structures.

Keywords

(almost) contact structures, $G_2$ structures

2010 Mathematics Subject Classification

53C38, 53D10, 53D15, 57R17

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Published 5 July 2013