Variational properties of the integrated mean curvatures of tubes in symmetric spaces (Q1600017)

The authors consider the tubular hypersurface \(P_t\) of radius \(t\) of a submanifold \(P\) in a symmetric space of arbitrary rank, and obtain various relationships between the integrated mean curvatures of \(P_t\) and their derivatives with respect to \(t\). Special emphasis is given to the structural differences between the cases of arbitrary rank and rank one. Contents include: an introduction, geodesic balls in symmetric spaces; tubes around totally geodesic submanifolds, tubes around principal orbits, and comparison theorems and variational problems. The paper concludes with a bibliography of fourteen items which provide a comprehensive overview of the topic.