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

Erhan Güler; Nurettin Cenk Turgay

doi:10.1007/s00009-019-1333-y

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

Erhan Güler^*, Nurettin Cenk Turgay

^*Corresponding author for this work

Department of Mathematics Engineering

Bartin University

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We consider rotational hypersurface in the four-dimensional Euclidean space E ⁴ . We study the Gauss map G of rotational hypersurface in 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 G satisfying L ₁ G= AG for some 4 × 4 matrix A are the hyperplanes, right circular hypercones, circular hypercylinders, and hyperspheres.

Original language	English
Article number	66
Journal	Mediterranean Journal of Mathematics
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s00009-019-1333-y
Publication status	Published - 1 Jun 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Keywords

Cheng–Yau operator
Euclidean spaces
finite type mappings
L -operators
rotational hypersurfaces

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10.1007/s00009-019-1333-y

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abstract = " We consider rotational hypersurface in the four-dimensional Euclidean space E 4 . We study the Gauss map G of rotational hypersurface in 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 G satisfying L 1 G= AG for some 4 × 4 matrix A are the hyperplanes, right circular hypercones, circular hypercylinders, and hyperspheres.",

keywords = "Cheng–Yau operator, Euclidean spaces, finite type mappings, L -operators, rotational hypersurfaces",

author = "Erhan G{\"u}ler and Turgay, {Nurettin Cenk}",

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AU - Güler, Erhan

AU - Turgay, Nurettin Cenk

PY - 2019/6/1

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N2 - We consider rotational hypersurface in the four-dimensional Euclidean space E 4 . We study the Gauss map G of rotational hypersurface in 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 G satisfying L 1 G= AG for some 4 × 4 matrix A are the hyperplanes, right circular hypercones, circular hypercylinders, and hyperspheres.

AB - We consider rotational hypersurface in the four-dimensional Euclidean space E 4 . We study the Gauss map G of rotational hypersurface in 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 G satisfying L 1 G= AG for some 4 × 4 matrix A are the hyperplanes, right circular hypercones, circular hypercylinders, and hyperspheres.

KW - Cheng–Yau operator

KW - Euclidean spaces

KW - finite type mappings

KW - L -operators

KW - rotational hypersurfaces

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DO - 10.1007/s00009-019-1333-y

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SN - 1660-5446

VL - 16

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 3

M1 - 66

ER -

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

Abstract

Bibliographical note

Keywords

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