Extensions in affine spaces of bilinear applications, differentiable actions, and tensors - Ostos Cordero, Benito Leonardo (2024)
In this article, several generalizations in affine spaces are studied. First, the notion of affine mappings to bilinear mappings defined in affine spaces is explored, referred to as affine bilinear mappings. Subsequently, differentiable actions of a Lie group on affine spaces are defined, and their isotropy group, orbit space, and set of fixed points are examined. Finally, the concept of tensor product between vector spaces is extended to the tensor product between affine spaces.