MANNHEIM CURVES IN 3-DIMENSIONAL SPACE FORMS

Bubbletons in 3-dimensional space forms

We construct constant mean curvature (CMC) bubbleton surfaces in the three-dimensional space forms R, S and H using the DPW method. We show that bubbletons in S and H have properties analogous to the properties of bubbletons in R. In particular, we give explicit parametrizations in all three space forms, and we show that the parallel CMC surface is congruent to the original bubbleton in all thr...

No Null-Helix Mannheim Curves in the Minkowski Space E13

In the study of the fundamental theory and the characterizations of space curves, the related curves for which there exist corresponding relations between the curves are very interesting and important problems. The most fascinating examples of such curve are associated curves, the curves for which at the corresponding points of them one of the Frenet vectors of a curve coincides with the one of...

Generalized Timelike Mannheim Curves in Minkowski Space - Time E 41

some characterizations for legendre curves in the 3-dimensional sasakian space

in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

Surfaces of constant curvature in 3-dimensional space forms

The study of surfaces immersed in a 3-dimensional ambient space plays a central role in the theory of submanifolds. In addition, Riemannian manifolds with constant sectional curvature can be considered as the most simple examples. Thus, one can think of surfaces with constant Gauss curvature in the Euclidean space R, hyperbolic space H or 3-sphere S as very natural objects of study. Through the...