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We present the TCFH of 11-dimensional supergravity and so demonstrate thatthe form bilinears of supersymmetric solutions satisfy a generalisation of theconformal Killing-Yano equation with resepct to the TCFH connection. We alsocompute the Killing-St\"ackel, Killing-Yano and closed conformal Killing-Yanotensors of all spherically symmetric M-branes that include the M2-brane,M5-brane, KK-monopole and pp-wave and demonstrate that their geodesic flows arecompletely integrable by giving all independent conserved charges ininvolution. We then find that all form bilinears of pp-wave and KK-monopolesolutions generate (hidden) symmetries for spinning particle probes propagatingon these backgrounds. Moreover, there are Killing spinors such that some of the1-, 2- and 3-form bilinears of the M2-brane solution also generate symmetriesfor spinning particle probes. We also explore the question on whether the formbilinears are sufficient to prove the integrability of particle probe dynamicson 11-dimensional supersymmetric backgrounds.

TCFHs, hidden symmetries and M-theory backgrounds