Consider the surface in $\mathbb R^{n+1}$ $$H=\left\{(x^1,\cdots,x^{n+1})\in\mathbb R^{n+1}\mid\sum_{i=1}^n(x^i)^2-(x^{n+1})^2=-1,x^{n+1}>0\right\}$$ Prove that the tensor field
$$h=\sum_{i=1}^n\mathrm dx^i\otimes\mathrm dx^i-\mathrm dx^{n+1}\otimes\mathrm dx^{n+1}$$ restricted to $H$ is a Riemann metric, and compute the sectional curvature.
I tried to use the coordinate $(u_1,\cdots,u_n,\sqrt{1+u_1^2+\cdots+u_n^2})$ to prove $h\vert_H$ is positive definite, but it is too difficult to compute curvature. Please help me.