In this paper the equiform differential geometry of curves in the pseudo-Galilean space G3 is introduced. Basic invariants and a moving trihedron are described. Frenet formulas are derived and the fundamental theorem of curves in equiform geometry of G3 is proved. The curves of constant curvatures are described.

In the present paper, we study rotational surfaces in the three dimensional pseudo-Galilean space G3. Also, we characterize rotational surfaces in G3 in terms of the position vector field, Gauss map and Laplacian operator of the second fundamental form on the surface.

Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of these properties is the Galilean symmetry, i.e. the invariance under Galilean transformations. In this paper, a mechanism to incorporate Galilean invariance in classical water wav...

We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We show these Cartan connections admit a form of normal coordinates, and that in...

In this study, we give the curves and tubular surfaces in Galilean space with modified orthogonal frame. Firstly, consider any curve G3 obtain derivative formulas of frame G3. Therefore, get surface Consequently, some examples figures.

A complete set of Equivalent Space-Time Theories based on a group of “equivalent” transformations has been studied by Selleri. This “equivalent” set of space-time theories includes Special Relativity Theory involving the Lorentz transformations and a semi-classical Absolute Space Theory based on the generalized Galilean or inertial transformations. In order to separate these theories, the light...

It is well known that the Galilei algebra is a sub algebra of Poincare algebra in one space dimension more. 1 This fact allows us to relate relativistic Poincare and Galilean theories. An interesting point is that Galilei transformations in two space dimensions are contained in the usual Poincare transformations? This enables us to present Poincare spin zero wavefunctions as Fourier transforms ...