Non-Riemannian Geometry

By L. Eisenhart. 2005

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Differential Geometry of Special Mappings (2019, methodology): “As we have seen, we can give an algorithm (known already to classics of differential geometry, [51,394]) that provides a solution, and may be implemented to a simple computer program.”
Stellar structure models in modified theories of gravity: Lessons and challenges (2019, background): “nforces the projective invariance of the theory, namely, under transformations Γλ µν→ Γλµν +ξµδλν, which is nothing buta manifestation ofthe freedom we have in parametrizing particle’s geodesic paths [437]. This requirement safeguards RBGs from the presence of ghost-like instabilities [438]. For the”
Survey on Affine Spheres (2008, background): “A partial converse is also true ([57] or [25]):”
On geodesic mappings of manifolds with affine connection (2009, background): “A manifold An = (M,∇) with affine connection admits a geodesic mapping onto Ān = (M, ∇̄), if and only if the Levi-Civita equation holds [1, 3, 10, 14]: ∇̄XY = ∇XY + ψ(X)Y + ψ(Y )X, (2) where ∇ and ∇̄ are the affine connections of An and Ān respectively, and ψ is a linear form.”