التفاصيل البيبلوغرافية
| العنوان: |
A relation between the curvature ellipse and the curvature parabola. |
| المؤلفون: |
Riul, P. Benedini1 benedini@usp.br, Sinha, R. Oset2 raul.oset@uv.es |
| المصدر: |
Advances in Geometry. Jul2019, Vol. 19 Issue 3, p389-399. 11p. |
| مصطلحات موضوعية: |
*CURVATURE, *PARABOLA, *GEOMETRIC surfaces, *CONIC sections, *ELLIPSES (Geometry), *GEOMETRY |
| مستخلص: |
At each point in an immersed surface in R4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in R3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in R4 to R3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface inR4 at a certain point to the geometry of the projection of the surface toR3 at the singular point. In particular we relate the curvature ellipse of the surface to the curvature parabola of its singular projection. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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