Extrinsic Symmetries of Parallel Transport

摘要

Let (M~n, g) and (M~(n+m), g) be two (semi-)Riemannian manifolds with dimension n and n + m and with respective Levi-Civita connections ▽ and ▽. Let f : (M, g) → (M,g) be an isometric immersion, i.e., let M~n be a submanifold of M~(n+m).