7 problems

Conjecture on three-quarters supersymmetry. There exist backgrounds with $\nu=\tfrac34$ which are not locally homogeneous.

Let $\tilde a=0,\ldots,3$ label four-dimensional Lorentzian gamma matrices, and decompose the six-dimensional spinor as $\boldsymbol{\epsilon}^1=\zeta\otimes\eta$, where $\zeta$ is…

The paper considers an interaction whose reasonable features suggest a gravitational interpretation. Twistor–graviton/gravitino conjecture. The resulting twistors should be related…

Let $\mu\neq 0$. Consider the class of spin manifolds in $\mathcal{M}(n,\Lambda,i_0,d)$, where the parameters and the spectral quantity…

Let $(M,g,J)$ be a Kähler spin manifold, and let an imaginary Kählerian Killing spinor mean a non-trivial spinor satisfying the corresponding imaginary Kählerian Killing spinor equ…

Uniqueness conjecture. Up to covering, $\mathbb{H}^{2n-1}$ is the only Lorentzian Sasakian manifold having non-zero imaginary Killing spinors lying pointwise in these middle eigens…

Algebraic solvability conjecture. This purely algebraic equation could be solved with an appropriate ansatz for the differential forms $F^i$. The conjecture concerns constructing s…