Classifications of Rotation Surfaces in Pseudo-Euclidean Space

Kim, Young Ho; Yoon, Dae Won

doi:10.4134/jkms.2004.41.2.379

Cited by 31 publications

(29 citation statements)

References 7 publications

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“…is called the Gauss map of M that is a smooth map which assigns to a point p in M the oriented (m − n)-plane through the origin of E m t and parallel to the normal space of M at p, [16]. We put ε = ν, ν = ε n+1 ε n+2 · · · ε m = ±1 and…”

Section: Prelimineriesmentioning

confidence: 99%

Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

Bektaş

Dursun

2015

Filomat

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Abstract.In this work, we focus on a class of timelike rotational surfaces in Minkowski space E 4 1 with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat timelike rotational surface of elliptic and hyperbolic types with pointwise 1-type Gauss map of the first and second kind. We also prove that there exists no flat timelike rotational surface of parabolic type in E 4 1 with pointwise 1-type Gauss map.

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Section: Prelimineriesmentioning

confidence: 99%

Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

Bektaş

Dursun

2015

Filomat

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“…Therefore, we can identify n+1 E m s+1 with some pseudo-Euclidean space E N q for some positive integer q where N = m n+1 [17].…”

Section: Pseudo-hyperbolic Gauss Mapmentioning

confidence: 99%

On Submanifolds of Pseudo-Hyperbolic Space with 1-Type Pseudo-Hyperbolic Gauss Map

Yeğin¹,

Dursun²

2016

Z. mat. fiz. anal. geom.

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“…Classify hypersurfaces in E n+1 with L r -1-type Gauss map. On the other hand, rotational surfaces of Euclidean spaces and pseudo-Euclidean spaces with pointwise 1-type Gauss map have been studied in several papers [9,12,14,20]. For example, in [9] In this paper, our aim is to study the hypersurfaces of revolution of a Euclidean space E n+1 in terms of L r -pointwise 1-type Gauss map of the first and second kind.…”

Section: Introductionmentioning

confidence: 99%

Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map

Mohammadpouri

2018

B Soc Paran Mat

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In this paper, we study hypersurfaces in E n+1 which Gauss map G satisfies the equation LrG = f (G + C) for a smooth function f and a constant vector C, where Lr is the linearized operator of the (r + 1)th mean curvature of the hypersurface, i.e., Lr(f ) = tr(Prwhere Pr is the rth Newton transformation, ∇ 2 f is the Hessian of f , LrG = (LrG 1 , . . . , LrG n+1 ), G = (G 1 , . . . , G n+1 ). We show that a rational hypersurface of revolution in a Euclidean space E n+1 has Lr-pointwise 1-type Gauss map of the second kind if and only if it is a right n-cone.

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Classifications of Rotation Surfaces in Pseudo-Euclidean Space

Cited by 31 publications

References 7 publications

Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

On Submanifolds of Pseudo-Hyperbolic Space with 1-Type Pseudo-Hyperbolic Gauss Map

Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map

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