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.


53C22 Geodesics in global differential geometry
53C55 Global differential geometry of Hermitian and Kählerian manifolds
Full Text: DOI EuDML