*Houston Journal of MathematicsĀ *30 (2004), no. 1, 55–87. Joint with

Weiqing Gu.

In this work, which lead to my undergraduate thesis and written jointly with my undergraduate advisor, I studied Cayley 4-submanifolds of 8-dimensional Euclidean space. TheseĀ are certain calibrated submanifolds, and play a role in string theory and itsĀ generalizations. The main technique was to use 3-dimensional subgroup of Spin(7) to simplify and solve the PDEs defining these Cayley 4-manifolds.