Abstract We connect certain continuous motions of discrete planar curves resulting in semi-discrete potential Korteweg–de Vries (mKdV) equation with Darboux transformations smooth curves. In doing so, we define infinitesimal that include the aforementioned motions, and also give an alternate geometric interpretation for establishing mKdV equation.

The conformal transformation in the Einstein Hilbert action leads to a new frame where an extra scalar degree of freedom is compensated by the local conformal-like symmetry. We write down a most general action resulting from such transformation and show that it covers both general relativity and conformally coupled to gravity scalar field as the particular cases. On quantum level the equivalenc...

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

In this work, we consider the Lie's method of infinitesimal transformation groups and discrete symmetries method for Burgers equation with time dependent flux at the origin. Following the Lie's method of infinitesimal transformation groups we determine the symmetry reductions and similarity solutions of the governing equation. By applying discrete symmetries analysis we have obtained three grou...

Based on the de Broglie-Bohm relativistic quantum theory of motion we show that the conformal formulation of general relativity, being linked with a Weyl-integrable geometry, may implicitely contain the quantum effects of matter. In this context the Mach's principle is discussed. In recent papers [1,2] the singularity problem has been treated from a point of view that is based upon the conforma...

ABS’I’RACI’. Pseudo-Sasakian manifolds M(U,E,,,g) endowed wlth a contact conformal connection are defined. It is proved tlat sucl manifolds are space forms M(K),K < O, and somo remarkable properttos of the 1,ie algebra of infinitesimal transformatton. of the principal vector feld U on M are discussed. Properties of tle leaves of a co-tsotroptc foliation on I’! and properties of the tangent bund...

We show in the framework of Pfaff systems theory, the functional dependences of the general analytic solutions of a suitable system of involutive differential equations describing the differences between the analytic solutions of the conformal and “Poincaré” Lie equations. Then we ascribe to the infinitesimal variations of the parametrizing functionals some physical meanings as the electromagne...

In this study, we located and compared different types of horizons in the spherically symmetric Vaidya solution. The horizons we found were trapping horizons, which can be null, timelike, or spacelike, null surfaces with constant area change and also conformal Killing horizons. The conformal Killing horizons only exist for certain choices of the mass function. Under a conformal transformation, ...