Killing spinor-valued forms and the cone construction

Petr Somberg and Petr Zima

Address: Petr Zima, Petr Somberg, Mathematical Institute of Charles University, Sokolovská 83, Praha 8 - Karlín, Czech Republic,


Abstract: On a pseudo-Riemannian manifold $\mathbb{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $\mathbb{M}$ and parallel fields on the metric cone over $\mathbb{M}$ for spinor-valued forms.

AMSclassification: primary 53C15; secondary 35R01, 53C27, 81R25.

Keywords: pseudo-Riemannian spin manifolds, Killing type equations, cone construction, spinor-valued differential forms.

DOI: 10.5817/AM2016-5-341