This paper defines two new extrinsic curvature quantities on the corner of a four-dimensional Riemannian manifold with corner. One these is pointwise conformal invariant, and transformation other governed by linear second-order conformally invariant partial differential operator. The Gauss-Bonnet theorem then stated in terms quantities.

We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This so-called differential radical characterization relies on a sound abstraction of the reachable set of solutions by the smallest variety that contains it. The characterization leads to a differential radical invar...

We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This so-called differential radical characterization relies on a sound abstraction of the reachable set of solutions by the smallest variety that contains it. The characterization leads to a differential radical invar...

A model potential for two-particle relativistic systems is investigated in the framework of Poincare-invariant quantum mechanics (or relativistic Hamiltonian dynamics). The potential considered allows to reduce the main integro-differential equation of Poincare-invariant quantum mechanics to the equation analogous to the radial equation and have analytical solution for relativistic bound system...

This is the first in a series of papers devoted to the development and applications of a new general theory of moving frames. In this paper, we formulate a practical and easy to implement explicit method to compute moving frames, invariant differential forms, differential invariants and invariant differential operators, and solve general equivalence problems for both finite-dimensional Lie grou...

We use the theory of reduction of exterior differential systems with symmetry to study the problem of using a symmetry group of a differential equation to find non-invariant solutions.

Hamiltonian mechanics is given an invariant formulation in terms of Geometric Calculus, a general differential and integral calculus with the structure of Clifford algebra. Advantages over formulations in terms of differential forms are explained.