Nearly half-flat $\rm{SU}(3)$-structures on $S^3\times S^3$

Ragini Singhal

Nearly half-flat $\rm{SU}(3)$-structures on $S^3\times S^3$

Differential Geometry 2024-09-05 v2

Authors: Ragini Singhal

Abstract

We study the $\rm{SU}(3)$ -structure induced on an oriented hypersurface of a 7-dimensional manifold with a nearly parallel $\rm{G}_2$ -structure. We call such $\rm{SU}(3)$ -structures nearly half-flat. We characterise the left invariant nearly half-flat structures on $S^3\times S^3$ . This characterisation then help us to systematically analyse nearly parallel $\rm{G}_2$ -structures on an interval times $S^3\times S^3$ .

Keywords

almost contact manifolds quasi-isometry holonomy

Cite

@article{arxiv.2310.11233,
  title  = {Nearly half-flat $\rm{SU}(3)$-structures on $S^3\times S^3$},
  author = {Ragini Singhal},
  journal= {arXiv preprint arXiv:2310.11233},
  year   = {2024}
}

Comments

17 pages. To appear in Differential Geometry and its Applications

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