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

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Bartin University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

11 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Makale numarası	66
Dergi	Mediterranean Journal of Mathematics
Hacim	16
Basın numarası	3
DOI'lar	https://doi.org/10.1007/s00009-019-1333-y
Yayın durumu	Yayınlandı - 1 Haz 2019

Bibliyografik not

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Belgeye Erişim

10.1007/s00009-019-1333-y

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "Cheng–Yau Operator and Gauss Map of Rotational Hypersurfaces in 4-Space",

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, L -operators, finite type mappings, rotational hypersurfaces",

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

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

month = jun,

day = "1",

doi = "10.1007/s00009-019-1333-y",

language = "English",

volume = "16",

journal = "Mediterranean Journal of Mathematics",

issn = "1660-5446",

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TY - JOUR

T1 - Cheng–Yau Operator and Gauss Map of Rotational Hypersurfaces in 4-Space

AU - Güler, Erhan

AU - Turgay, Nurettin Cenk

PY - 2019/6/1

Y1 - 2019/6/1

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 - L -operators

KW - finite type mappings

KW - rotational hypersurfaces

UR - https://www.scopus.com/pages/publications/85064557692

U2 - 10.1007/s00009-019-1333-y

DO - 10.1007/s00009-019-1333-y

M3 - Article

AN - SCOPUS:85064557692

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

Özet

Bibliyografik not

Belgeye Erişim

Diğer Dosyalar ve Linkler

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