Associative Submanifolds of the 7-Sphere

Details Associative Submanifolds of the 7-Sphere Associative Submanifolds of the 7-Sphere

2010-06-02

arxiv.org/abs/1006.0361v1

Mathematics

Differential Geometry

52 pages

Scientific paper

We perform the first major study of associative submanifolds in the 7-sphere, which are minimal 3-dimensional submanifolds associated with the natural G_2 structure on the 7-sphere. We classify the associative 3-folds which arise as group orbits and those with constant curvature. We also describe the associative 3-folds satisfying the curvature condition known as Chen's equality using the theory of ruled associative 3-folds. Finally, we produce one-parameter families of non-congruent isometric associative submanifolds in the 7-sphere satisfying Chen's equality from general minimal 2-spheres in the 6-sphere.

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