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Nearly Parallel G2-structures with Large Symmetry Group
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- Journal:
- Canadian Journal of Mathematics / Volume 73 / Issue 2 / April 2021
- Published online by Cambridge University Press:
- 16 December 2019, pp. 339-359
- Print publication:
- April 2021
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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.
Cohomogeneity One Randers Metrics
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- Journal:
- Canadian Mathematical Bulletin / Volume 59 / Issue 3 / 01 September 2016
- Published online by Cambridge University Press:
- 20 November 2018, pp. 575-584
- Print publication:
- 01 September 2016
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- Article
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An action of a Lie group
$G$ on a smooth manifold 
$M$ is called cohomogeneity one if the orbit space 
${M}/{G}\;$ is of dimension 1. A Finsler metric 
$F$ on $M$ is called invariant if $F$ is invariant under the action of $G$. In this paper, we study invariant Randers metrics on cohomogeneity one manifolds. We first give a sufficient and necessary condition for the existence of invariant Randers metrics on cohomogeneity one manifolds. Then we obtain some results on invariant Killing vector fields on the cohomogeneity one manifolds and use them to deduce some sufficient and necessary conditions for a cohomogeneity one Randers metric to be Einstein.
