A geometrical interpretation of Okubo Spin group

Some geometrical properties of the oscillator group

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

A geometrical interpretation of the inverse matrix

A New Geometrical Interpretation of Trilinear Constraints

We give a new geometrical interpretation of the well-known algebraic trilinear constraints used in motion analysis from three views observation. We show that those algebraic equations correspond to depth errors appropriately weighted by a function of the relative reliability of the corresponding measurements. Therefore directly minimizing the algebraic trilinear equations, in the least squares ...

Geometrical Interpretation of Constrained Systems

The standard approach to classical dynamics is to form a Lagrangian which is a function of n generalized coordinates qi, n generalized velocities q̇i and parameter τ . The 2n variables qi, q̇i form the tangent bundle TQ. The passage from TQ to the cotangent bundle T ∗Q is achieved by introducing generalized momenta and a Hamiltonian. However, this procedure requires that the rank of Hessian matrix

Geometrical interpretation of solutions of certain PDEs

In §1 the authors define the notion of harmonic map between two generalized Lagrange spaces. In §2 it is proved that for certain systems of differential or partial differential equations, the solutions belong to a class of harmonic maps between two generalized Lagrange spaces. §3 describes the main properties of the generalized Lagrange spaces constructed in §2. These spaces, being convenient r...