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Main Title: Cubic form geometry for surfaces in S^3(1)
Author(s): Lusala, Tsasa
Type: Research Paper
Abstract: We consider the traceless part $\widehat{C}$ of the difference tensor field $C$ between the Levi-Civita connections of the first and the second fundamental forms for non-degenerate surface immersions in $\S^3(1)$. In analogy to affine differential geometry of $\mathbb{R}^{n+1}$ where quadrics are characterized by the vanishing of the traceless cubic form, we study the condition $\widehat{C}=0$, give examples and classify non-degenerate surfaces in $S^3(1)$ which satisfy this condition.
Subject(s): non-degenerate surfaces in 3-spheres
principal curvature functions
rotational surfaces
cubic form geometry
Issue Date: 10-Dec-2000
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 53B25 Local submanifolds
53A15 Affine differential geometry
35-04 Explicit machine computation and programs
53C24 Rigidity results
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2000, 676
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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