Abstract:
Given a hypersurface immersion and a transversal vector field, the formula of Gauss
leads to an induced connection and a symmetric bilinear function called affine
fundamental form. We define the norm of tensor field using the affine fundamental
form (assumed to be nondegenerate) and prove that a hypersurface immersion on a
connected compact 𝑛-dimensional differential manifold 𝑀 into the affine space
ℝ𝑛+1 induces an almost affinely flat structure on 𝑀.
