Cheng–Yau Operator and Gauss Map of Rotational Hypersurfaces in 4-Space

  • Erhan GülerEmail author
  • Nurettin Cenk Turgay


We consider rotational hypersurface in the four-dimensional Euclidean space \( {\mathbb {E}}^{4}\). We study the Gauss map \(\mathbf {G}\) of rotational hypersurface in \({\mathbb {E}}^{4}\) with respect to the so-called Cheng–Yau operator \(L_{1}\) acting on the functions defined on the hypersurfaces. We obtain the classification theorem that the only rotational hypersurface with Gauss map \(\mathbf {G}\) satisfying \(L_{1}\mathbf {G}=\mathbf {AG}\) for some \( 4\times 4\) matrix \(\mathbf {A}\) are the hyperplanes, right circular hypercones, circular hypercylinders, and hyperspheres.


Euclidean spaces Cheng–Yau operator finite type mappings rotational hypersurfaces \(L_{k}\)-operators 

Mathematics Subject Classification

Primary 53A35 Secondary 53C42 



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Authors and Affiliations

  1. 1.Department of Mathematics Faculty of SciencesBartın UniversityBartınTurkey
  2. 2.Department of Mathematics Faculty of Science and LettersIstanbul Technical UniversityIstanbulTurkey

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