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A spectral estimate for the Dirac operator on Riemannian flows. (English) Zbl 1221.53054

The authors derive a new upper bound for the smallest eigenvalues of the Dirac operator on an \(n+1\)-dimensional Riemannian manifold admitting a flow having transversal Killing spinors. They also derive an estimate for Sasaki \(n\)- and \(3\)-dimensional manifolds, and give a partial classification in the limiting case. Their estimates are also compared with a lower bound in terms of a natural tensor depending on the eigenspinor.
Contents include: Introduction; Preliminaries; Main theorem; Case of Sasakian manifolds; The 3-dimensional case; Classification of limiting manifolds; Comparison with a lower bound of the spectrum; and References (twenty-four items).

MSC:

53C12 Foliations (differential geometric aspects)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C27 Spin and Spin\({}^c\) geometry
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P15 Estimates of eigenvalues in context of PDEs
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References:

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