Spin c -structures and Dirac operators on contact manifolds - Petit, Robert (Differential geometry and its applications, 2005)
Any contact metric manifold has a Spin c -structure. Thus, we study on any Spin c -spinor bundle of a contact metric manifold, Dirac type operators associated to the generalized Tanaka–Webster connection. Bochner–Lichnerowicz type formulas are derived in this setting and vanishing theorems are obtained.