differential geometry help

hi my friends ı have some questions for you;

1.The standart curvature tensor R,for the unit sphere is parallel.

2.$\displaystyle \kappa_\sigma$ depends only a $\displaystyle \sigma$(not on generators)

3.a)if if n=2,then every metric is an Einstein metric(HİNT:$\displaystyle R=K.R_1$)

b)Spaces of constant curvature are all EİNSTEİN spaces(HİNT:same reason)

some new questions ı could not solve

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 $\displaystyle R^4$ be given by the equation

M={$\displaystyle (x_1,x_2,x_3,x_4)\in R^4\mid x_1^2+x_2^2=x_3^2+x_4^2=1$} 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=$\displaystyle S^1xS^1$ where $\displaystyle S^1$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.