Abstract
In this paper we show that the space of spinors over a warped product over S-1 has a certain splitting GammaSigma = circle plusW(k,n) in spaces of spinors of weight k and winding number n which is respected by the Dirac operator. The same holds for the space of functions and the Laplace operator. We give eigenvalue estimates for the eigenvalues lambda(k,n) of the Dirac operator with eigenspinors ...
Abstract
In this paper we show that the space of spinors over a warped product over S-1 has a certain splitting GammaSigma = circle plusW(k,n) in spaces of spinors of weight k and winding number n which is respected by the Dirac operator. The same holds for the space of functions and the Laplace operator. We give eigenvalue estimates for the eigenvalues lambda(k,n) of the Dirac operator with eigenspinors of weight k and winding number n and eigenvalues mu(m,n) of the Laplace operator with eigenfunctions of weight m and winding number n. In particular, we show that mu(k,n)(2)greater than or equal tolambda(k,n)(2) holds for large n on S(1)x(fT)(l) where T-l is a flat torus with the trivial spin structure.
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