A brief note on the spectrum of the basic Dirac operator
نویسندگان
چکیده
In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M,F) with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O’Neill tensor and the first eigenvalue of the Dirac operator on M . We discuss examples and also define a new version of the basic Laplacian whose spectrum does not depend on the choice of bundle-like metric.
منابع مشابه
1 4 Se p 20 08 A brief note on the spectrum of the basic Dirac operator
In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M,F) with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O’Neill tensor and the first eigenvalue of the Dirac operator on M . We discuss examples and also define a new version of the basic Laplacian wh...
متن کاملInverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...
متن کاملThe Spectrum of Basic Dirac Operators
In this note, we discuss Riemannian foliations, which are smooth foliations that have a transverse geometric structure. We explain a known generalization of Dirac-type operators to transverse operators called “basic Dirac operators” on Riemannian foliations, which require the additional structure of what is called a bundle-like metric. We explain the result in [10] that the spectrum of such an ...
متن کاملPrescribing Eigenvalues of the Dirac Operator
In this note we show that every compact spin manifold of dimension ≥ 3 can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity 1.
متن کاملOn the fine spectra of the generalized difference operator Delta_{uv} over the sequence space c0
The main purpose of this paper is to detemine the fine spectrum of the generalized difference operator Delta_{uv} over the sequence space c0. These results are more general than the fine spectrum of the generalized difference operator Delta_{uv} of Srivastava and Kumar.
متن کامل