Some Associative Submanifolds of the Squashed 7-Sphere

kawai, kotaro;

The squashed 7-sphere S7 is a 7-sphere with an Einstein metric given by the canonical variation and its cone R8 − {0} has full holonomy Spin(7). There is a canonical calibrating 4-form  on R8 − {0}. A minimal 3-submanifold in S7 is called associative if its cone is calibrated by . In this paper, we classify two types of fundamental associative submanifolds in the squashed S7. One is obtained by the intersection with a 4-plane and the other is homogeneous. Then we study their infinitesimal associative deformations and explicitly show that all of them are integrable.