Repository: DepositOnce â€“ institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - RPRT
AU - Lusala, Tsasa
PY - 2000
TI - Cubic form geometry for surfaces in S^3(1)
DO - 10.14279/depositonce-14735
UR - http://dx.doi.org/10.14279/depositonce-14735
PB - Technische UniversitÃ¤t Berlin
LA - en
AB - 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.
KW - non-degenerate surfaces in 3-spheres
KW - principal curvature functions
KW - rotational surfaces
KW - cubic form geometry
ER -