5 problems

Let $M^n$ be an immersed submanifold of a real space form with constant sectional curvature $\kappa$. The normalized scalar curvature is denoted by $\rho$, the normalized normal sc…

Let $\Sigma\subset\mathbb S^n$ be a closed, orientable, connected embedded hypersurface, and let $H$ denote its mean curvature. For $x\in\mathbb S^n$, define … where…

DDVV conjecture.

Let $M^n$ be an $n$-dimensional manifold isometrically immersed in the space form $N^{n+m}(c)$ of constant sectional curvature $c$. Let $h$ be the second fundamental form, let…

Let $M^n$ be an immersed submanifold of the space form $N^{n+m}(c)$, with scalar curvature $\rho$, normal scalar curvature $\rho^{\perp}$, and mean curvature tensor…