Existence and uniqueness of volume-minimizing cycles in Grassmann manifolds
In this thesis, I prove existence, nonexistence and uniqueness theorems for volume-minimizing 4-dimensional cycles calibrated by the first Pontryagin form in low-dimensional Grassmann manifolds. To do this, I build bridges connecting the following subjects: (1) volume-minimizing cycles in Grassmann manifolds, (2) fibrations of round spheres by great subspheres, (3) linearly independent tangent vector fields on spheres, and then cross the bridges in various directions to gain new understanding of these subjects.
Pan, Liu-Hua, "Existence and uniqueness of volume-minimizing cycles in Grassmann manifolds" (1992). Dissertations available from ProQuest. AAI9235185.