The Hessian of the distance from a surface in the Heisenberg group

none2Given a smooth surface S in the Heisenberg group, we compute the Hessian of the function measuring the Carnot-Charathéodory distance from S in term of the Mean Curvature of S and of "an imaginary curvature" which was introduced in: Metric normal and distance function in the Heisenberg group", MATHEMATISCHE ZEITSCHRIFT. vol. 256, pp. 661 - 684, in order to find the geodesics which are metrically normal to S. Explicit formulae are given when S is a plane or the metric sphere.L'articolo è disponibile anche in rete al seguente indirizzo web http://mathstat.helsinki.fi/Annales/Vol33/vol33.htmlnoneN. Arcozzi; F. FerrariN. Arcozzi; F. Ferrar