the present paper is concerned with the generalization of the holditch theorem under oneparameterhomothetic motion on lorentzian planes. in this paper, for the homothetic lorentzian motion, weexpressed the steiner formula. furthermore, we present the holditch-type theorems.

in this paper the concept of homothetic dual exponential motions in d3 is discussed and theirvelocities obtained. due to the way in which the matter is presented, the paper gives some formula and factsabout dual exponential motions which are not generally known

it is easily seen that a motion and a homothetic transformation are both affine collineations and that an affine collineation preserves the curvature tensor. In [l ] one of the present authors proved that in a space of nonzero constant curvature a mapping preserving curvature is a motion. For an Einstein space with nonzero curvature scalar, a mapping preserving Ricci curvature is a motion; for ...

We make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces revolution and ruled in R3. prove that MCF non-cylindrical R3 are trivial. Moreover, we characterize revolutions under a homothetic helicoidal motion terms generating curve. Finally, cylindrical Explicit families exact also given.

Metric symmetries have always played a large role in the development of exact solutions to the Einstein field equations. Often a choice of metric symmetry is made based on an assumed symmetry of the matter distribution, i.e., spherical symmetry for astrophysical objects or cylindrical symmetry for a simple string. A homothetic motion ~homothety! describes the symmetry of scale transformations, ...

In this paper we analyzed the problem of investigating locally the scalar curvature of the two dimensional kinematic surfaces foliated by the homothetic motion of an eight curve in LorentzMinkowski 5-space . We express the scalar curvature of the corresponding two dimensional kinematic surfaces as the quotient of hyperbolic functions { }. From that point, we derive the necessary and sufficient ...

The Equations of motion of vortex sources (examined earlier by Fridman and Polubarinova) are studied, and the problems of their being Hamiltonian and integrable are discussed. A system of two vortex sources and three sources-sinks was examined. Their behavior was found to be regular. Qualitative analysis of this system was made, and the class of Liouville integrable systems is considered. Parti...