2 problems

Let $\tilde{Y}$ be a $(1,2)$-tensor field on $\mathbb S^3$. Say that $\tilde{Y}(p)$ is a positive cross tensor at each point $p\in\mathbb S^3$, and let $T(g)$ denote the $(1,2)$-te…

Let $\mathbb S^3$ be the three-sphere, let $Y$ be a positive-definite symmetric $(0,2)$-tensor field on $\mathbb S^3$, and let $X(g)$ denote the cross curvature tensor of a Riemann…