Photovoltaic module electrical termination design requirement study

On the Isothermal Geometry of Corrugated Graphene Sheets

“…The difference tensor Q can be decomposed into the so-called contorsion tensor K, expressing the difference between the Christoffel symbols of a metric-compatible part of the covariant derivative ∇ and the Levi-Civita covariant derivative ∇ a and defined by [23]:…”

“…Definition 1 introduces a distinguished surface form. Let us consider, basing oneself o the papers [23] and [33], the problem of compatibility of the covariant derivative ∇ and the general volume element ω. We are dealing, as it was mentioned at the beginning of this section, with the inelastically distorted graphene sheets.…”

“…[1]) and dimM = n. It, in turn, can be essential if the defective crystals theory is developed as a field theory consistent with the material geometry described by the triple (∇, ω, a) of geometrical objects. An example of using volume form compatible with a covariant derivative for minimal action principle is discussed in [23] and [33]. If a is the metric tensor of eq.…”

“…follows that, in the Riemannian space M a = (M, a), a volume (surface if n = 2) form ω is compatible with the covariant derivative ∇ if and only if[23] …”

“…Theorem 1[23] Let M be a differentiable manifold endowed with the metric a and a covariant derivative ∇. Let % = &ω a , where φ is a smooth positive scalar on M, be a volume form on M. Then, for every vector field…”