1-)Define the curvature tensor as a(1,3) tensor and calculate its covariant derivative in the direction of X,where X is a fixed vector field.

2-)let a subset M of be given by the equation

M={ } prove that M is a two-dimensional differentiable manifold without displaying an ATLAS.(ı don'T know how to show without ATLAS)

i just think that M= where is 1 manifold hence the cross product is two manifold but how can ı show in the language of mathematic.

i hope some body help me,please i need some help here.