Geometry of skeletal structures and symmetry sets
Azeb Alghanemi · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · 2012
In this thesis we study the geometry of symmetry sets and skeletal structures. The relationship between a symmetry point (skeletal point) and the associated midlocus point is studied and the impact of the singularity of the radius function on this relationship is investigated. Moreover, the concept of the centroid set associated to a smooth submanifold of Rn+1 is introduced and studied. Also, the relationship between the shape operator of a skeletal structure at a smooth point and the shape operator of its boundary at the associated point is studied.