The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds
Uwe Semmelmann (Stuttgart)
Abstract: The Rarita-Schwinger operator is a twisted Dirac operator.
It has several interesting applications in physics and differential
geometry. In my talk I will introduce this operator, give some of
its properties and then concentrate on its kernel. In contrast to
the classical Dirac operator the Rarita-Schwinger operator can have
a non-trivial kernel on compact manifolds with positive scalar curvature.
I will discuss several examples and in particular explain how one can
identify the kernel of the Rarita-Schwinger operator with subspaces
of harmonic forms on manifolds with special holonomy.
My talk is based on a joint work with Yasushi Homma (Waseda University, Tokyo).