Minimal submanifolds in Riemannian spin manifolds with parallel spinor fields (Q1602440)

The author studies certain minimal submanifolds in a Riemannian spin manifold with parallel spinor field. Results from the submanifold theory of Dirac operators given by Ch. Bär are exposed. In the following chapter the author derives a Lichnerowicz type formula for even-dimensional Riemannian spin submanifolds of arbitrary codimensions. This formula is applied to give a complete characterization of minimal hypersurfaces \(M^{2n}\) in a \((2n+1)\)-dimensional Riemannian spin manifold with a nonzero parallel spinor field. A special chapter is devoted to minimal surfaces in a four-dimensional flat torus or hyper-Kähler manifold.