Bundle Constructions of Calibrated Submanifolds in R^7 and R^8

@article{Ionel2004BundleCO,
  title={Bundle Constructions of Calibrated Submanifolds in R^7 and R^8},
  author={Marianty Ionel and Spiro Karigiannis and Maung Min-Oo},
  journal={Mathematical Research Letters},
  year={2004},
  volume={12},
  pages={493-512}
}
We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R^{2n}. 
Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections
Mean curvature flows in manifolds of special holonomy
Calibrated Subbundles in Noncompact Manifolds of Special Holonomy
The stability of the mean curvature flow in manifolds of special holonomy
Calibrated Submanifolds.
Deformation theory of asymptotically conical coassociative 4‐folds
...
1
2
...

References

SHOWING 1-10 OF 14 REFERENCES
Deformations of calibrated submanifolds
Compact Manifolds with Special Holonomy
Ricci-flat metrics on the complexification of a compact rank one symmetric space
The exceptional holonomy groups and calibrated geometry
Lectures on special Lagrangian geometry
Deformations of G 2 and Spin(7) Structures
Mirror symmetry is T duality
Constructing Associative 3-folds by Evolution Equations
...
1
2
...