A differential equation related with some general connections
A general connection Γ on a differentiable manifold M n is given as a geometrical object with components (Pi jTi jh) in local coordinates (ui) such that (P i j ) are the components of a tensor and (Ti j) satisfy the rules : Γ< _ dv’ f p k g V M0vT\ Jh ~ duk \ 1 dvidvh + lmdvi dvh J ’ where T i j are the second components of Γ in local coordinates (vi). We call a point of M n is regular or singular with respect to Γ if det (P i j ) ≠ 0 or = 0, respectively. We say a curve γ(t) = (u i (t)) is a geodesic with respect to Γ if u i (t) satisfy the equations: ni d2v? „, du* duh „ and the parameter t is called its affine parameter.
KeywordsScalar Curvature Galerkin Method Hyperbolic Space Ricci Tensor Nonlinear Partial Differential Equation
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