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Nearly Parallel G2-structures with Large Symmetry Group

Part of: Global differential geometry

Published online by Cambridge University Press:  16 December 2019

Fabio Podestà
Fabio Podestà*
Affiliation:
Dipartimento di Matematica e Informatica “Ulisse Dini”, Università di Firenze, V.le Morgagni 67/A, 50100 Firenze, Italy Email: fabio.podesta@unifi.it
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Abstract

We prove the existence of a one-parameter family of nearly parallel G2-structures on the manifold $\text{S}^{3}\times \mathbb{R}^{4}$, which are mutually non-isomorphic and invariant under the cohomogeneity one action of the group SU(2)3. This family connects the two locally homogeneous nearly parallel G2-structures that are induced by the homogeneous ones on the sphere S7.

Keywords

Nearly parallel G2-structurescohomogeneity one actionsEinstein metrics

MSC classification

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C30: Homogeneous manifolds
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 2 , April 2021 , pp. 339 - 359
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Copyright
© Canadian Mathematical Society 2019

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