Constant angle spacelike surface in de Sitter space S₁³

Tugba Mert,Baki Karlıga

doi:10.5269/bspm.v35i3.24398

Abstract

In this paper; using the angle between unit normal vector field of surfaces and a fixed spacelike axis in R₁⁴, we develop two class of spacelike surface which are called constant timelike angle surfaces with timelike and spacelike axis in de Sitter space S₁³.

Highlights

Let x : M −→ S13 be a immersion and let ξ be a timelike unit normal vector field to M
Differential geometry of curves and surfaces are summarized in de Sitter space S13
Let R41 be 4-dimensional vector space equipped with the scalar product, which is defined by x, y = −x1y1 + x2y2 + x3y3 + x4y4

Summary

Differantial Geometry of de Sitter Space S13

Differential geometry of curves and surfaces are summarized in de Sitter space S13. Let R41 be 4-dimensional vector space equipped with the scalar product , which is defined by x, y = −x1y1 + x2y2 + x3y3 + x4y4. In [2], [3] and [5] Izimuya at all introduced and investigated differantial geometry of curves and surfaces Hyperbolic 3-space. Ki± (p) and Ki (p), (i = 1, 2) are called hyperbolic and de Sitter principal curvatures of M at p = x (u0). We consider the hyperbolic curvature vector k (s) = t′ (s) − γ (s) and the de Sitter normal curvature. The de Sitter normal curvature depends only on the point p and the unit tangent vector of M at p analogous to the Euclidean case.

Constant Timelike Angle Spacelike Surfaces

Tangent Surface with Spacelike Axis