The Casimir Operator of a Metric Connection with Skew-symmetric Torsion
نویسنده
چکیده
For any triple (M, g,∇) consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator Ω acting on spinor fields. In case of a naturally reductive space and its canonical connection, our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly Kähler, cocalibrated G2-structures) admit unique connections with skew-symmetric torsion. We study the corresponding Casimir operator and compare its kernel with the space of ∇-parallel spinors.
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