Killing-Yano equations and G-structures

Understand

We solve the Killing-Yano equation on manifolds with a $G$-structure for $G=SO(n), U(n), SU(n), Sp(n)\cdot Sp(1), Sp(n), G_2$ and $Spin(7)$.

• Solutions include nearly-K\"ahler, weak holonomy $G_2$, balanced SU(n) and holonomy $G$ manifolds.
• As an application, we find that particle probes on $AdS_4\times X$ compactifications of type IIA and 11-dimensional supergravity admit a ${\cal W}$-type of symmetry generated by the fundamental forms.
• We also explore the ${\cal W}$-symmetries of string and particle actions in heterotic and common sector supersymmetric backgrounds.