Application of spaces of subspheres to conformal invariants of curves and canal surfaces

Rémi Langevin, Jun O'Hara, and Shigehiro Sakata. "Application of spaces of subspheres to conformal invariants of curves and canal surfaces." Annales Polonici Mathematici 108.2 (2013): 109-131. <http://eudml.org/doc/280452>.

@article{RémiLangevin2013,
abstract = {We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation allows for the re-expression of the conformal invariants in terms of standard Euclidean invariants.},
author = {Rémi Langevin, Jun O'Hara, Shigehiro Sakata},
journal = {Annales Polonici Mathematici},
keywords = {conformal curvature; conformal torsion; canal surface; channel surface; osculating circle; osculating sphere},
language = {eng},
number = {2},
pages = {109-131},
title = {Application of spaces of subspheres to conformal invariants of curves and canal surfaces},
url = {http://eudml.org/doc/280452},
volume = {108},
year = {2013},
}

TY - JOUR
AU - Rémi Langevin
AU - Jun O'Hara
AU - Shigehiro Sakata
TI - Application of spaces of subspheres to conformal invariants of curves and canal surfaces
JO - Annales Polonici Mathematici
PY - 2013
VL - 108
IS - 2
SP - 109
EP - 131
AB - We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation allows for the re-expression of the conformal invariants in terms of standard Euclidean invariants.
LA - eng
KW - conformal curvature; conformal torsion; canal surface; channel surface; osculating circle; osculating sphere
UR - http://eudml.org/doc/280452
ER -