Sentence examples for canonical connection from inspiring English sources

A key idea is the introduction of a canonical connection, matching the manifold and group properties of the configuration space.

There is also a corresponding formal notion of a canonical connection.

Thus we obtain a second canonical connection for (T^{1,0}_X), namely the Levi-Čivita connection.

If (nabla ) is flat (as it is in the case of a canonical connection) the curvature tensor is identically zero.

In particular, each local loop (F) gives rise to a right alternative infinitesimal loop, which is the geodesic loop of the canonical connection of (F).

The operation (cdot ) defines a local loop on (Usubseteq M) and it is a straightforward check that (nabla ) is its canonical connection.

Following this approach, the N-connection and the bulk of fundamental geometric structures (metric, canonical linear connection, almost symplectic and almost complex structures...) are derived in general form starting from regular (for simplicity) Lagrangian and/or Hamiltonian.

On the tangent bundle ({T} G) there exists a canonical flat connection (nabla ).

The canonical d-connection and the Levi-Civita connection.

We note that this metrization procedure contains additional covariant derivations of the d-metric coefficients, defined by arbitrary d-connection, not only N-adapted derivatives of the d-metric and N-connection coefficients as in the case of the canonical d-connection.

where R ^ ßγ Open image in new window is the curvature 2-form for the canonical d-connection, ϒ a denote all possible sources defined by using the canonical d-connection, and η ÷ * 1 Open image in new window is the volume form with the Hodje operator '*', η a α e a ⅃ η Open image in new window, η αβ ÷ e ß ⅃ η a Open image in new window, α αβγ ÷ e ⅃ η α αβ,... Open image in new window.