Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2017.09.05
  • Accepted : 2018.03.27
  • Published : 2018.07.01
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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.

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References

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