Kwang-Soon Park
Abstract
Let M be a simply connected complete K?hler manifold and N a closed complete totally geodesic complex submanifold of M such that every minimal geodesic in N is minimal in M. Let U? be the unit normal bundle of N in M. We prove that if a distance function ? is differentiable at v ? U?, then ? is also differentiable at -v.
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Let M be a simply connected complete K?hler manifold and N a closed complete totally geodesic complex submanifold of M such that every minimal geodesic in N is minimal in M. Let U? be the unit normal bundle of N in M. We prove that if a distance function ? is differentiable at v ? U?, then ? is also differentiable at -v.
Key concepts: Submanifold, Differentiable function, Geodesic, Mathematics, Manifold (fluid mechanics), Pure mathematics, Function (biology), Combinatorics