The submanifold compatibility equations in magnetic geometry

Abstract

With the notions of magnetic curvature and magnetic second fundamental form recently introduced by Assenza and Albers-Benedetti-Maier, respectively, we establish analogues of the Gauss, Ricci, and Codazzi-Mainardi compatibility equations from submanifold theory in the magnetic setting.

Minor corrections and improvements after referee reports. To appear in Annals of Global Analysis and Geometry