The submanifold compatibility equations in magnetic geometry

Key Points

• This research aims to establish compatibility equations in the context of magnetic geometry using newly defined concepts.
• Introduced concepts of magnetic curvature and magnetic second fundamental form.
• Established analogues of Gauss, Ricci, and Codazzi–Mainardi equations.
• Applied submanifold theory to magnetic settings.
• Formulated compatibility equations analogous to classical ones.
• Demonstrated the application of magnetic curvature in these equations.
• Provided a new perspective on the interplay between geometry and magnetic fields.