Construction of Coassociative Submanifolds

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


The notion of coassociative submanifolds is defined as the special class of the minimal submanifolds in G 2-manifolds. In this talk, we introduce the method of [5] to construct coassociative submanifolds by using the symmetry of the Lie group action. As an application, we give explicit examples in the 7-dimensional Euclidean space and in the anti-self-dual bundle over the 4-sphere.


Vector Bundle Cell Complex Levi Civita Connection Orbit Space Stereographic Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author is grateful to the organizers for the opportunity of talking in 2014 ICM Satellite Conference on “Real and Complex Submanifolds” and the 18th International Workshop on Differential Geometry. The author would like to congratulate Prof. Young Jin Suh on being selected seventeen distinguished mathematicians of Korea by the National Academy of Sciences.


  1. 1.
    Bryant, R.L., Salamon, S.M.: On the construction of some complete metrics with exceptional holonomy. Duke Math. J. 58, 829–850 (1989)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Fernández, M., Gray, A.: Riemannian manifolds with structure group G 2. Ann. Mat. Pura Appl. 32(4), 19–45 (1982)CrossRefGoogle Scholar
  3. 3.
    Harvey, R., Lawson, H.B.: Calibrated geometries. Acta Math. 148, 47–157 (1982)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Hashimoto, K., Sakai, T.: Cohomogeneity one special Lagrangian submanifolds in the cotangent bundle of the sphere. Tohoku Math. J. 64, 141–169 (2012)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Hsiang, W.Y., Lawson, H.B.: Minimal submanifolds of low cohomogeneity. J. Differ. Geom. 5, 1–38 (1971)MATHMathSciNetGoogle Scholar
  6. 6.
    Kawai, K.: Construction of coassociative submanifolds in \(\mathbb{R}^{7}\) and Λ 2 S 4 with symmetries. arXiv:1305.2786 [math.DG] (preprint)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Mathematical InstituteTohoku UniversitySendaiJapan

Personalised recommendations