Existence of Optimal Flat Ribbons.

We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in can be extended to an infinitely narrow flat ribbon having bending energy. We also show that, in general, minimizers are not free of planar points, yet such points must be isolated under the mild condition that the torsion does not vanish.

Planar Pseudo-geodesics and Totally Umbilic Submanifolds.

We study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e.

Total torsion of three-dimensional lines of curvature.

A curve in a Riemannian manifold is if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically. In particular, when lies on an oriented hypersurface of , we say that is if the curve's principal normal, its torsion vector, and the surface normal are everywhere coplanar. Suppose that is three-dimensional and closed.

Classification of Rank-One Submanifolds.

We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold , we associate an integer-valued function, called , measuring the extent to which fails to be cylindrical. In particular, we show that if the degree is constant and equal to , then the singularities of can only occur along an -dimensional "striction" submanifold.

Cartan ribbonization and a topological inspection.

We develop the concept of Cartan ribbons together with a rolling-based method to ribbonize and approximate any given surface in space by intrinsically flat ribbons. The rolling requires that the geodesic curvature along the contact curve on the surface agrees with the geodesic curvature of the corresponding Cartan development curve. Essentially, this follows from the orientational alignment of the two co-moving Darboux frames during rolling.

On the Prototyping of an ICT-Enhanced Toilet System for Assisting Older Persons Living Independently and Safely at Home.

Standard toilets often do not meet the needs of a significant number of older persons and persons with disabilities. The EU funded iToilet project aims at design and development of a new type of ICT enhanced modular toilet system which shall be able to support autonomy, dignity and safety of older persons living at home. Methodologically the project started with gathering user requirements by means of questionnaires, interviews and focus group discussion involving a total of 74 persons, thereof 41 subjects with movement disorders (primary users), 21 caregivers (secondary users) and 12 healthcare managers (tertiary users).