Flächen im isotropen s2×ℝ
Tóm tắt
In [4] the author published the theory of curves in isotropic S2 × ℝ. New results of Pottmann [1] show, that isotropic geometry has a meaning in CAGD, especially in questions on scattered data and visualisation. These are not only considered in euclidean space, but also on manifolds. So it may be interesting to look at the theory of surfaces in isotropic manifolds. This will be done in this paper for the manifold S2 × ℝ by embedding it in I4. Special surfaces on isotropic S2 × ℝ will be geometrically interpreted.
Tài liệu tham khảo
POTTMANN, H.:Curvature Analysis and Visualization for Functions Defined on Euclidean Spaces or Surfaces, 1992, Preprint
RASCHEWSKI, P.K.:Riemannsche Geometrie und Tensoranalysis. VEB Deutscher Verlag der Wissenschaften 1959
SACHS, H.:Isotrope Geometrie des Raumes, Friedrich Vieweg & Sohn Verlag, Braunschweig/Wiesbaden 1990.
SPITZMÜLLER, K.:Isotrope Geometrie auf S2 × ℝ, Dissertation, Karlsruhe 1990.
VOGEL, W.O.:Quasisymmetrische lineare Zusammenhänge in Mannigfaltigkeiten mit singulärer Riemannscher Metrik, Bericht Nr. 224 der Math.-Stat. Sektion im Forschungszentrum Graz (1983).