On Generalized Constant Ratio Surfaces of Higher Codimension

Alev Kelleci; Nurettin Cenk Turgay; Mahmut Ergüt

doi:10.1007/s00009-019-1376-0

On Generalized Constant Ratio Surfaces of Higher Codimension

Alev Kelleci^*, Nurettin Cenk Turgay, Mahmut Ergüt

^*Corresponding author for this work

Department of Mathematics Engineering

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

1 Citation (Scopus)

Abstract

In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces E⁴. Then, we get complete local classification of CS surfaces in E⁴. We also study GCR surfaces in terms of some of its geometrical invariants.

Original language	English
Article number	95
Journal	Mediterranean Journal of Mathematics
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s00009-019-1376-0
Publication status	Published - 1 Aug 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

Funding

This paper is a part of Ph.D. thesis of the first named author who was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) as a Ph.D. scholar.

Funders	Funder number
TUBITAK
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Keywords

Euclidean spaces
canonical principal direction
constant slope surfaces
generalized constant ratio submanifolds
position vector

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10.1007/s00009-019-1376-0

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abstract = "In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces E4. Then, we get complete local classification of CS surfaces in E4. We also study GCR surfaces in terms of some of its geometrical invariants.",

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AU - Turgay, Nurettin Cenk

AU - Ergüt, Mahmut

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N2 - In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces E4. Then, we get complete local classification of CS surfaces in E4. We also study GCR surfaces in terms of some of its geometrical invariants.

AB - In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces E4. Then, we get complete local classification of CS surfaces in E4. We also study GCR surfaces in terms of some of its geometrical invariants.

KW - Euclidean spaces

KW - canonical principal direction

KW - constant slope surfaces

KW - generalized constant ratio submanifolds

KW - position vector

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ER -

On Generalized Constant Ratio Surfaces of Higher Codimension

Abstract

Bibliographical note

Funding

Keywords

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