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On the differentiability of a distance function. (English) Zbl 1199.53097

The author proves that if a distance function \(\rho\) is differentiable at \(v\in U_\nu\), then \(\rho\) is also differentiable at \(-v\), where \(U_\nu\) is the unit normal bundle of a closed complete totally geodesic complex submanifold of a simply connected complete Kähler manifold, such that every minimal geodesic in this submanifold is minimal in the manifold. Several ideas for further research are also presented.

MSC:

53C22 Geodesics in global differential geometry
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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