Surface pencil with a common line of curvature in Minkowski 3-space

Construction of a surface pencil with a common special surface curve

In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $vec{W}_{0} $ of a surface curve $vec{r}(s)$ and unit surface normal $vec{n} $ along the curve $vec{r}(s)$ satisfy the condition $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. We point out that a $D$-type curve is a geodesic curve or an...

The harmonic evolute of a surface in Minkowski 3-space

In this paper we describe harmonic evolutes of surfaces in Minkowski 3-space. In particular, we study properties of harmonic evolutes of constant mean curvature surfaces and their relation to parallel surfaces. Furthermore, we study harmonic evolutes of surfaces of revolution. AMS subject classifications: 53A35, 53B30

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Bisectors in Minkowski 3-Space

We discuss the concept of the bisector of a segment in a Minkowski normed n-space. We prove that all bisectors are topological images of a plane of the embedding Euclidean 3-space iff the shadow boundaries of the unit ball K are topological circles. To a conjectured proving strategy for dimensions n, we introduce the concept of general parameter sphere of the unit ballK, corresponding to a dire...

Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space

which gives an isometric embedding of the hyperbolic space H into R. Hano and Nomizu [11] were probably the first to observe the non-uniqueness of isometric embeddings of H in R by constructing other (geometrically distinct) entire solutions of (1.1)–(1.2) for n 1⁄4 2 (and c1 1) using methods of ordinary di¤erential equations. Using the theory of Monge-Ampère equations, A.-M. Li [12] studied en...