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J. Korean Math. Soc. 2018; 55(4): 987-1004

Online first article May 30, 2018      Printed July 1, 2018

https://doi.org/10.4134/JKMS.j170580

Copyright © The Korean Mathematical Society.

Centroaffine geometry of ruled surfaces and centered cyclic surfaces in $\mathbb R^4$

Yun Yang, Yanhua Yu

Northeastern University, Northeastern University

Abstract

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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

MSC numbers: 53A15, 53C42, 58E30

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