相关论文: Timelike $B_2$-slant helices in Minkowski space $E…
A simple algebraic global isometric embedding is presented for the nonrotating BTZ black hole and its counterpart of Euclidean signature. The image of the embedding, in Minkowski space of two extra dimensions, is the interection of two…
Consider the energy $E_\alpha[\Sigma]=\int_\Sigma |p|^\alpha\, d\Sigma$, where $\Sigma$ is a surface in Euclidean space $\r^3$ and $\alpha\in\r$. We prove that planes and spheres are the only stationary surfaces for $E_\alpha$ with constant…
We characterize the biharmonic curves in the special linear group $SL(2,R)$. In particular, we show that all proper biharmonic curves in $SL(2,R)$are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean…
The paper proposes a generalization of the Park transform based on the Frenet frame, which is a special set of coordinates defined in differential geometry for space curves. The proposed geometric transform is first discussed for three…
A focal representation of a generic regular curve {\gamma} in E^{m+1} consists of the centers of the osculating hyperplanes. A k-slant helix {\gamma} in E^{m+1} is a (generic) regular curve whose unit normal vector V_{k} makes a constant…
In this paper, we first consider a class of expanding flows of closed, smooth, star-shaped hypersurface in Euclidean space $\mathbb{R}^{n+1}$ with speed $u^\alpha f^{-\beta}$, where $u$ is the support function of the hypersurface, $f$ is a…
We use Generalized Fermi-Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We…
We present a cyclic symmetric space-time, admitting closed time-like curves (CTCs) which appear after a certain instant of time, i. e., a time-machine space-time. These closed time-like curves evolve from an initial spacelike hypersurface…
General $(\alpha, \beta)$ norms are an important class of Minkowski norms which contains the original $(\alpha, \beta)$ norms. In this note, by studying the behavior of the Darboux curves of the indicatrix, we give a characterization of…
The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a…
The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of…
We propose the model of massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle follow from the fact that all the classical paths of the particle lie on a cylinder whose position in…
We consider a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with timelike or spacelike axis. We call these surfaces meridian surfaces of elliptic or…
We study the geometry of curves in the Minkowski space and in the de Sitter space, specially at points where the tangent direction is lightlike (i.e. has length zero) called lightlike points of the curve. We define the focal sets of these…
The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space manifolds. In the homogeneous case, a time-space manifold is a…
In this paper, we investigate a curve whose spherical image the tangent indicatrix and binormal indicatrix is slant helix and called it as a slant helix. We obtain that the spherical images are spherical slant helices defined by [3]. This…
In this paper, we study the Dirichlet problem for a class of prescribed curvature equations in Minkowski space. We prove the existence of smooth spacelike hypersurfaces with a class of prescribed curvature and general boundary data based on…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
In this paper we study the general affine geometry of curves in affine space $A^2$. For a regular plane curves we define two kinds of moving frames. The first is of minimal order in all moving frames.The second is the Frenet moving frame.…
In this paper, we consider an expanding flow of closed, smooth, uniformly convex hypersurface in Euclidean \mathbb{R}^{n+1} with speed u^\alpha f^\beta (\alpha, \beta\in\mathbb{R}^1), where u is support function of the hypersurface, f is a…