4 problems

Let $\mathcal{M}$ be a compact manifold, let $\mathfrak{g}$ be the relevant finite-dimensional algebra, for example $E_{d(d)}$, and let $L^{2}(\mathcal{M})$ provide a basis. Let…

Let $M$ be a 2-step nilmanifold with abelian complex structure. Suppose that there exists an ascending basis … such that $d\omega^{n+1}$ is non-degenerate. Let $\Gamma_1\in H^2(M)$…

Bivector-potential conjecture. The potential of $R$-flux is conjectured to be given by a bivector field $\beta$.

Let a generalized Sasakian manifold define a supersymmetric $AdS_5$ solution of type IIB supergravity, and let its generalized Sasakian structure have contact volume. The dual four…