Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space $${\mathbb{E}^4}$$

Dursun, Uğur; Turgay, Nurettin Cenk

doi:10.1007/s00009-011-0167-z

Cited by 18 publications

(17 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also note that the surfaces given in Example 5.7 and Example 5.8 are members of a larger family of surfaces studied by Dursun and Turgay in [21,22].…”

Section: Special Slant Surfaces On Almost Constant Curvature Manifoldsmentioning

confidence: 91%

Special proper pointwise slant surfaces of a locally product Riemannian manifold

Gülbahar¹,

Kılıç²,

Çelik³

2015

Turk J Math

View full text Add to dashboard Cite

The structure of pointwise slant submanifolds in an almost product Riemannian manifold is investigated and the special proper pointwise slant surfaces of a locally product manifold are introduced. A relation involving the squared mean curvature and the Gauss curvature of pointwise slant surface of a locally product manifold is proved. Two examples of proper pointwise slant surfaces of a locally product manifold, one of which is special and the other one is not special, are given.

show abstract

“…We also note that the surfaces given in Example 5.7 and Example 5.8 are members of a larger family of surfaces studied by Dursun and Turgay in [21,22].…”

Section: Special Slant Surfaces On Almost Constant Curvature Manifoldsmentioning

confidence: 91%

Special proper pointwise slant surfaces of a locally product Riemannian manifold

Gülbahar¹,

Kılıç²,

Çelik³

2015

Turk J Math

View full text Add to dashboard Cite

show abstract

“…On the other hand, pseudo-umbilical submanifolds are also well-known and have been studied in many articles, [6,14,5].…”

Section: Introductionmentioning

confidence: 99%

On Pseudo-Umbilical Rotational Surfaces with Pointwise 1-type Gauss Map in $\mathbb{E}^4_2$

Canfes¹,

Dursun²,

Bektaş³

2017

Proceedings Book of International Workshop on Theory of Submanifolds

View full text Add to dashboard Cite

Abstract. In this work, we study two families of rotational surfaces in the pseudo-Euclidean space E 4 2 with profile curves lying in 2-dimensional planes. First, we obtain a classification of pseudo-umbilical spacelike surfaces and timelike surfaces in these families. Then, we show that in this classification there exists no a pseudo-umbilical rotational surface in E 4 2 with pointwise 1-type Gauss map of second kind. Finally, we determine such pseudo-umbilical rotational surfaces in E 4 2 having pointwise 1-type Gauss map of first kind.

show abstract

“…For the surfaces of revolution in R 3 , it is easy to define the parametrization of the surfaces with constant Gaussian curvature. In recent years some mathematicians have taken an interest in the surfaces of revolution in R 4 , for example V. Milosheva ([6]), U. Dursun and N. C. Turgay ( [3]), K. Arslan ([1]), . .…”

Section: Introductionmentioning

confidence: 99%

“…In [4], V. Milosheva applied invariance theory of surfaces in the four dimensional Euclidean space to the class of general rotational surfaces whose meridians lie in two-dimensional planes in order to find all minimal super-conformal surfaces. These surfaces were further studied by U. Dursun and N. C. Turgay in [3], which found all minimal surfaces by solving the differential equation that characterizes minimal surfaces. They then determined all pseudo-umbilical general rotational surfaces in R 4 .…”

Section: Introductionmentioning

confidence: 99%

Surfaces of Revolution With Constant Gaussian Curvature in Four-Space

Cuong

2013

Asian-European J. Math.

View full text Add to dashboard Cite

In this paper, we show that the constant property of the Gaussian curvature of surfaces of revolution in both R 4 and R 4 1 depend only on the radius of rotation. We then give necessary and sufficient conditions for the Gaussian curvature of the general rotational surfaces whose meridians lie in two dimensional planes in R 4 to be constant, and define the parametrization of the meridians when both the Gaussian curvature is constant and the rates of rotation are equal.Mathematics Subject Classification. 53A05, 53C50, 53A35.

show abstract

Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space $${\mathbb{E}^4}$$

Cited by 18 publications

References 7 publications

Special proper pointwise slant surfaces of a locally product Riemannian manifold

Special proper pointwise slant surfaces of a locally product Riemannian manifold

On Pseudo-Umbilical Rotational Surfaces with Pointwise 1-type Gauss Map in $\mathbb{E}^4_2$

Surfaces of Revolution With Constant Gaussian Curvature in Four-Space

Contact Info

Product

Resources

About