On the infinitesimal isometries of manifolds with Killing spinors

Abstract : We study the Lie algebra of infinitesimal isometries of seven-dimensional simply connected manifolds with Killing spinors. We obtain some splitting theorems for the action of this algebra on the space of Killing spinors, and as a corollary we prove that there is no infinitesimal isometry of constant length on a seven-dimensional 3-Sasakian manifold (not isometric to a space form) except the linear combinations of the Sasakian vector fields.
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Andrei Moroianu. On the infinitesimal isometries of manifolds with Killing spinors. Journal of Geometry and Physics, Elsevier, 2000, 35, pp.63-74. ⟨10.1016/S0393-0440(99)00079-0⟩. ⟨hal-00126031⟩

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