Results 121 to 130 of about 256 (151)
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.
Uğur Dursun
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TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Bulletin of the Korean Mathematical Society, 2011 Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle c1 centered at origin with an Euclidean planar curve c2 has harmonic Gauss map if and only if M is a part of a plane ...
Betul Bulca +2 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 ...
Yusuf Yaylı, Yaylı Yusuf
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SURFACES OF REVOLUTION WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Journal of the Korean Mathematical Society, 2005 A submanifold \(M\) of a Euclidean or pseudo-Euclidean space is said to have pointwise 1-type Gauss map \(G\) if it satisfies \[ \Delta G=f(G+C), \] where \(\Delta\) is the Laplace operator corresponding to the induced metric on \(M\), \(f\) a function on \(M\), and \(C\) a constant vector.
Bang-Yen Chen, Young Ho Kim
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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.
Velichka Milousheva, Kadri Arslan
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HELICOIDAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Journal of the Korean Mathematical Society, 2009 The helicoidal surfaces with pointwise 1-type or harmonic gauss map in Euclidean 3-space are studied. The notion of pointwise 1- type Gauss map is a generalization of usual sense of 1-type Gauss map. In particular, we prove that an ordinary helicoid is the only genuine he- licoidal surface of polynomial kind with pointwise 1-type Gauss map of the flrst
Mie-Kyung Choi +2 more
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CLASSIFICATION OF RULED SURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
Taiwanese Journal of Mathematics, 2010 Ruled surfaces with the Gauss map satisfying a partial differential equation which is similar to an eigenvalue problem in a 3-dimensional Euclidean space are studied. Such a Gauss map is said to be of pointwise 1-type, namely, the Gauss map $G$ satisfies $\Delta G = f(G+C)$, where $\Delta$ is the Laplacian operator, $f$ is a non-zero function and $C ...
Young Ho Kim
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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.
Yusuf Yaylı, Yaylı Yusuf
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SURFACES WITH POINTWISE 1-TYPE GAUSS MAP [PDF]
The Pure and Applied Mathematics, 2011 In this article, we study generalized slant cylindrical surfaces (GSCS`s) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that GSCS`s with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only polynomial kind GSCS`s with ...
Kim Dong-Soo
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SHAPE OPERATOR AND GAUSS MAP OF POINTWISE 1-TYPE
Journal of the Korean Mathematical Society, 2015 Abstract. We examine the relationship of the shape operator of a sur-face of Euclidean 3-space with its Gauss map of pointwise 1-type. Sur-faces with constant mean curvature and right circular cones with respectto some properties of the shape operator are characterized when theirGauss map is of pointwise 1-type. 1.
Young Ho Kim
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