5 problems

Let $(G,g)$ be a semi-Riemannian Lie group with a subgroup $K$ generating a left-invariant conformal foliation $\mathcal F$ on $G$ of codimension two. Semisimple subgroup minimalit…

Let $n$ and $q$ be positive integers with $n \geq 2q$. Let $(M,g)$ be an $n$-dimensional geodesically complete semi-Riemannian manifold of index $q$, and suppose its sectional curv…

Let $B\times_f^{N}F$ be an $N$-warped product of a Riemannian manifold $B$, a positive warping function $f$, and a weighted Riemannian manifold $F$. The weighted semi-Riemannian an…

Projective Lichnerowicz–Obata conjecture. Either $G$ acts on $M$ by affine transformations, or $(M^n,g)$ is Riemannian with positive constant sectional curvature.

Let $M$ be a $(2n+1)$-dimensional semi-Riemannian space form $M_{1}^{2n+1}(c)$ of index $1$, and let $B$ be a $2n$-dimensional Riemannian manifold. A proper biharmonic semi-Riemann…