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http://dx.doi.org/10.4134/JKMS.j170580

CENTROAFFINE GEOMETRY OF RULED SURFACES AND CENTERED CYCLIC SURFACES IN ℝ4  

Yang, Yun (Department of Mathematics Northeastern University)
Yu, Yanhua (Department of Mathematics Northeastern University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.4, 2018 , pp. 987-1004 More about this Journal
Abstract
In this paper, we get several centroaffine invariant properties for a ruled surface in ${\mathbb{R}}^4$ with centroaffine theories of codimension two. Then by solving certain partial differential equations and studying a centroaffine surface with some centroaffine invariant properties in ${\mathbb{R}}^4$, we obtain such a surface is centroaffinely equivalent to a ruled surface or one of the flat centered cyclic surfaces. Furthermore, some centroaffine invariant properties for centered cyclic surfaces are considered.
Keywords
ruled surfaces; cyclic surfaces; Pick invariant; centroaffine transformation;
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