In this work we study spacelike and timelike surfaces of revolution in Minkowski space E1 that satisfy the linear Weingarten relation aH+bK = c, where H and K denote the mean curvature and the Gauss curvature of the surface and a, b and c are constants. The classification depends on the causal character of the axis of revolution. We will give a first integral of the equation of the generating c...

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E 1 are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike general helix. In terms of solution, we determine the parametric representation of the general helices from the intrin...

Scalar field theories with appropriate potentials in Minkowski space can have timedependent classical solutions containing topological defects which correspond to S-branes i.e. branes all of whose tangential dimensions are spacelike. It is argued that such Sbranes arise in string theory as time-dependent solutions of the worldvolume tachyon field of an unstable D-brane or D-brane-anti-D-brane p...

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or lightlike, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector fiel...

In this paper we obtain a sharp height estimate concerning compact spacelike hypersurfaces Σn immersed in the (n + 1)dimensional Lorentz–Minkowski space Ln+1 with some nonzero constant r-mean curvature, and whose boundary is contained into a spacelike hyperplane of Ln+1. Furthermore, we apply our estimate to describe the nature of the end of a complete spacelike hypersurface of Ln+1. © 2007 Els...

A local classification of spacelike surfaces in Minkowski 4-space, which are invariant under spacelike rotations, and with mean curvature vector either vanishing or light-like, is obtained. Furthermore, the existence of such surfaces with prescribed Gaussian curvature is shown. A procedure is presented to glue several of these surfaces with intermediate parts where the mean curvature vector fie...

Let Mn+p p (c) be n + p-dimensional connected semi-Riemannian manifold of constant curvature c whose index is p. It is called indefinite space form of index p. Let M be an n-dimensional Riemannian manifold immersed in Mn+p p (c). The semi-Riemannian metric of Mn+p p (c) induces the Riemannian metric of M , M is called a spacelike submanifold. Spacelike submanifolds in indefinite space form Mn+p...