On the infinitesimal isometries of manifolds with Killing spinors

Andrei Moroianu (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: Infinitesimal isometry; Killing spinor; Sasakian structure

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu. On the infinitesimal isometries of manifolds with Killing spinors. Journal of Geometry and Physics, 2000, 35, pp.63-74. ⟨10.1016/S0393-0440(99)00079-0⟩. ⟨hal-00126031⟩