scholarly journals Meridian Surfaces on Rotational Hypersurfaces with Lightlike Axis in ${\mathbb E}^4_2$

2017 ◽  
Author(s):  
Velichka Milousheva
Keyword(s):  
Lightlike Axis

The geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space

2016 ◽  
Vol 13 (10) ◽  
pp. 1650116 ◽  
Author(s):  
Derya Kahvecí ◽  
Yusuf Yayli ◽  
Ísmaíl Gök
Keyword(s):  
Rotation Angle ◽  
Rotation Axis ◽  
Symmetric Matrix ◽  
Unit Length ◽  
Exponential Map ◽  
Spatial Displacement ◽  
Split Quaternions ◽  
Rodrigues Formula ◽  
Lightlike Axis ◽  
The Given

The aim of this paper is to give the geometrical and algebraic interpretations of Euler–Rodrigues formula in Minkowski 3-space. First, for the given non-lightlike axis of a unit length in [Formula: see text] and angle, the spatial displacement is represented by a [Formula: see text] semi-orthogonal rotation matrix using orthogonal projection. Second, we obtain the classifications of Euler–Rodrigues formula in terms of semi-skew-symmetric matrix corresponds to spacelike, timelike or lightlike axis and rotation angle with the help of exponential map. Finally, an alternative method is given to find rotation axis and the Euler–Rodrigues formula is expressed via split quaternions in Minkowski 3-space.

scholarly journals MARGINALLY TRAPPED MERIDIAN SURFACES OF PARABOLIC TYPE IN THE FOUR-DIMENSIONAL MINKOWSKI SPACE

2013 ◽  
Vol 10 (10) ◽  
pp. 1350060 ◽  
Author(s):  
GEORGI GANCHEV ◽  
VELICHKA MILOUSHEVA
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Parabolic Type ◽  
Mean Curvature Vector ◽  
Spacelike Surface ◽  
Marginally Trapped Surface ◽  
Dimensional Minkowski Space ◽  
Trapped Surface ◽  
Lightlike Axis

A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We introduce meridian surfaces of parabolic type as one-parameter systems of meridians of a rotational hypersurface with lightlike axis in Minkowski 4-space and find their basic invariants. We find all marginally trapped meridian surfaces of parabolic type and give a geometric construction of these surfaces.

scholarly journals On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Minghao Jin ◽  
Donghe Pei ◽  
Shu Xu
Keyword(s):  
Gauss Map ◽  
Second Fundamental Form ◽  
Satisfy Condition ◽  
Real Matrix ◽  
De Sitter ◽  
Surfaces Of Revolution ◽  
3 Dimensional ◽  
The Second Fundamental Form ◽  
Dimensional Minkowski Space ◽  
Lightlike Axis

By studying the Gauss mapGand Laplace operatorΔhof the second fundamental formh, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of Enneper of the 3rd kind, the de Sitter pseudosphere, and the hyperbolic pseudosphere that satisfy conditionΔhG=ΛG, Λbeing a3×3real matrix.

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