Asian Journal of Mathematics

Existence of compatible contact structures on $G_2$-manifolds

M. Firat Arikan, Hyunjoo Cho, and Sema Salur

Full-text: Open access

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.

Article information

Source
Asian J. Math., Volume 17, Number 2 (2013), 321-334.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1383923853

Mathematical Reviews number (MathSciNet)
MR3078933

Zentralblatt MATH identifier
1337.53064

Subjects
Primary: 53C38: Calibrations and calibrated geometries 53D10: Contact manifolds, general 53D15: Almost contact and almost symplectic manifolds 57R17: Symplectic and contact topology

Keywords
(Almost) contact structures $G_2$ structures

Citation

Arikan, M. Firat; Cho, Hyunjoo; Salur, Sema. Existence of compatible contact structures on $G_2$-manifolds. Asian J. Math. 17 (2013), no. 2, 321--334. https://projecteuclid.org/euclid.ajm/1383923853


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