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Spectrum of twisted Dirac operators on the complex projective space \(\mathbb P^{2q+1}(\mathbb C)\). (English) Zbl 1212.53072

Summary: We explicitly determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles over the complex projective space \(\mathbb P^{2q+1}(\mathbb C)\) for \(q\geq 1\).

MSC:

53C35 Differential geometry of symmetric spaces
53C27 Spin and Spin\({}^c\) geometry
58C40 Spectral theory; eigenvalue problems on manifolds
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