naa a22 4500 510760791 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0086-3 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0086-3 Conformal invariants and spherical contacts of surfaces in ℝ4 [Elektronische Daten] [M. Romero-Fuster, E. Sanabria-Codesal] Based on the fact that conformal maps preserve contacts of surfaces with hyperspheres, we introduce the concept of strong principal lines on surfaces in ℝ4 and obtain conformally invariant differential 1-forms along them. The zeros of these 1-forms are respectively characterized as ridges (singularities of squared-distance functions of type A k ,k≥4) and higher order semiumbilics (singularities of type D k ,k≥5). As a consequence we obtain that any closed orientable surface generically immersed in ℝ4 has at least 2 semiumbilic points of type D 5. We provide geometrical interpretations of these conformally invariant 1-forms in terms of the geometry of curves induced in the 5-dimensional de Sitter space and in the 5-dimensional lightcone. Revista Matemática Complutense, 2011 Immersed surfaces nationallicence Curvature ellipse nationallicence Semiumbilics nationallicence Ridges nationallicence Conformal invariants nationallicence de Sitter space nationallicence Romero-Fuster M. Departament de Geometria i Topologia, Universitat de València, Burjassot, Valencia, Spain aut Sanabria-Codesal E. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain aut Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 215-240 1139-1138 26:1<215 2013 26 13163 https://doi.org/10.1007/s13163-011-0086-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0086-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Romero-Fuster M. Departament de Geometria i Topologia, Universitat de València, Burjassot, Valencia, Spain aut NATIONALLICENCE 700 1- Sanabria-Codesal E. Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Valencia, Spain aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 215-240 1139-1138 26:1<215 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer