Does anybody know how to solve it? I've done a lot of tries but I didn't succeeded
Let $\Bbb H^n=\{ (x_0,x_1,...,x_n)\in \Bbb R^{n+1}:x_0^2+x_1^2+...+x_n^2=-1,x_0>0\}$ and the symetric bilinear form $\langle\langle(v_0,v_1,...,v_n),(w_0,w_1,...,w_n)\rangle\rangle=-v_0w_0+v_1w_1+...+v_nw_n$ be, for each $v,w \in \Bbb R^{n+1}$.
The tangent space in each point is $T_p\Bbb H^n=\{v \in\Bbb R^{n+1}:\langle\langle v,p\rangle\rangle =0\}$.
Prove the bilinear form is positive when it is restricted to $T_p\Bbb H^n$ for each $p\in \Bbb H^n$ and prove that $\Bbb H^n$ Riemannian manifold.