Infinitesimal rigidity and flexibility of a non-symmetric affine connection space

Using recent work as a foundation, we have considered the infinitesimal deformations f : x i → x i + ε z i ( x j ) of a space L N with non-symmetric affine connection L j k i . On the basis of the non-symmetry of the connection, we use four kinds of covariant derivatives to express the Lie derivative and the deformations. The rigidities of the geometric objects (connection, tensors, curvature) are defined and analyzed using the Lie derivative.