Results 11 to 20 of about 14,054 (185)
ON SPACELIKE ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Bulletin of the Korean Mathematical Society, 2015 Abstract. In this paper, we study a class of spacelike rotational surfacesin the Minkowski 4-space E 41 with meridian curves lying in 2-dimensionalspacelike planes and having pointwise 1-type Gauss map. We obtain allsuch surfaces with pointwise 1-type Gauss map of the first kind.
Dursun, Uğur
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HYPERSURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Taiwanese Journal of Mathematics, 2007 In this paper we prove that an oriented hypersurface $M$ of a Euclidean space $E^{n+1}$ has pointwise 1-type Gauss map of the first kind if and only if $M$ has constant mean curvature. Then we conclude that all oriented isoparametric hypersurfaces of $E^{n+1}$ has 1-type Gauss map.
Uǧur Dursun
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VRANCEANU SURFACE IN E-4 WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
, 2011 In this article we investigate Vranceanu rotation surfaces with pointwise 1-type Gauss map in Euclidean 4-space E-4. We show that a Vranceanu rotation surface M has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficent conditions for Vranceanu rotation surface to have pointwise 1-type Gauss map.
Arslan, Kadri +5 more
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Flat Rotational Surfaces with Pointwise 1-Type Gauss Map Via Generalized Quaternions [PDF]
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2018 In this article, the authors consider a class of surfaces in \(\mathbb{R}^4\) endowed with the flat metric: \(g = dx_0^2 + \alpha dx_1^2 + \beta dx_2^2 + \alpha \beta dx_3^2,\) where \(\alpha, \beta\) are (nonzero) real numbers. The most important special cases are the Euclidean and split-signature cases, corresponding to \((\alpha,\beta)\) being \((1 ...
Kahraman Aksoyak, Ferdağ, Yaylı, Yusuf
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Rotational embeddings in E^4 with pointwise 1-type gauss map [PDF]
Turkish Journal of Mathematics, 2011 In the present article we study the rotational embedded surfaces in E4. The rotational embedded surface was first studied by G. Ganchev and V. Milousheva as a surface in E4. The Otsuki (non-round) sphere in E4 is one of the special examples of this surface.
Arslan, Kadri +5 more
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Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map [PDF]
Boletim da Sociedade Paranaense de Matemática, 2018 In this paper, we study hypersurfaces in $\E^{n+1}$ which Gauss map $G$ satisfies the equation $L_rG = f(G + C)$ for a smooth function $f$ and a constant vector $C$, where $L_r$ is the linearized operator of the $(r + 1)$th mean curvature of the hypersurface, i.e., $L_r(f)=tr(P_r\circ\nabla^2f)$ for $f\in \mathcal{C}^\infty(M)$, where $P_r$ is the $r ...
Akram Mohammadpouri
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Lorentzian Submanifolds in Semi-Euclidean Spaces with Pointwise 1-Type Gauss Map [PDF]
Geometry, Integrability and Quantization, 2016 In this work first, we survey the most recent classification results for submanifolds with pointwise 1-type Gauss map. Then, we study a class of hypersurfaces with vanishing Gauss-Kronecker curvature in terms of type of their Gauss map.
Turgay, Nurettin C.
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POINTWISE 1-TYPE GAUSS MAP OF DEVELOPABLE SMARANDACHE RULED SURFACES IN $\mathbb{E}^{3}$ [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2023 In this paper, we study developable TN, TB, and NB-Smarandache ruled surface with pointwise 1-type Gauss map. In particular, we obtain every such developable TN-Smarandache ruled surface has constant mean curvature, developable TB Smarandache ruled surface is minimal if and only if the curve is a planar curve or helix, and developable NB-Smarandache ...
Stuti - Tamta, Ram Shankar Gupta
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General rotational surfaces with pointwise 1-type Gauss map in pseudo-Euclidean space E 2 4 [PDF]
Indian Journal of Pure and Applied Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aksoyak, Ferdag Kahraman, Yayli, Yusuf
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Meridian Surfaces of Elliptic or Hyperbolic Type with Pointwise $1$-type Gauss Map in Minkowski $4$-space [PDF]
Taiwanese Journal of Mathematics, 2016 In the present paper we consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. They are called meridian surfaces of elliptic or hyperbolic type, respectively. We study these surfaces with respect to their Gauss map.
Arslan, Kadri, Milousheva, Velichka
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