English

Variation formulae for the volume of coassociative submanifolds

Differential Geometry 2025-01-03 v5

Abstract

We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of G2G_2 data. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds; this formula highlights the role of the ambient torsion and Ricci curvature. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non.

Keywords

Cite

@article{arxiv.2207.13956,
  title  = {Variation formulae for the volume of coassociative submanifolds},
  author = {Tommaso Pacini and Alberto Raffero},
  journal= {arXiv preprint arXiv:2207.13956},
  year   = {2025}
}

Comments

v.5: Minor changes. Final version, to appear in Annals of Global Analysis and Geometry