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Let $M$ be a smooth, pseudo-Riemannian manifold with $\dim(M) \ge 2.$ Let $\nabla$ be any affine connection on $M$. No reason for it to be the Levi-Civita connection. All we assume is that it has zero ...

Suppose that on a certain coordinate system the coefficients $\Gamma^i_{jk}$, $i,j,k=1,\cdots, n$, of a linear connection are constant. We do not require compatibility with a metric, however I am ...

I'm reading Nomizu & Sasaki's "Affine Differential Geometry: Geometry of Affine Immersions" and I'm having some trouble with Proposition 1.4. I have an immersed surface in $M \hookrightarrow \...