Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces

@article{Almorox2006HolomorphicSO,
  title={Holomorphic spectrum of twisted Dirac operators on compact Riemann surfaces},
  author={Antonio L{\'o}pez Almorox and Carlos Prieto},
  journal={Journal of Geometry and Physics},
  year={2006},
  volume={56},
  pages={2069-2091}
}
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References

SHOWING 1-10 OF 24 REFERENCES
The spectrum of twisted Dirac operators on compact flat manifolds
Let M be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles
Fourier coefficients of the resolvent for a Fuchsian group.
*~T + ~T~2~)~2ifc.y-r— acting on a Hubert space §k of automorphic forms dx dy) dx of weight k e IR. In this paper, we present the basic eigenfunction expansions of Gs k(z, z') and discuss
THE DIRAC OPERATOR ON HYPERSURFACES
Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here
Complex Abelian Varieties
Notation.- 1. Complex Tori.- 2. Line Bundles on Complex Tori.- 3. Cohomology of Line Bundles.- 4. Abelian Varieties.- 5. Endomorphisms of Abelian Varieties.- 6. Theta and Heisenberg Groups.- 7.
Non–trivial harmonic spinors on generic algebraic surfaces
We disprove Hitchin's conjecture to the effect that for a generic complex structure on a simply connected spin complex surface the square root of the canonical bundle has no more cohomology then is
Eigenvalues of the Kählerian Dirac Operator
We get estimates on the eigenvalues of the Kählerian Dirac operator in terms of the eigenvalues of the scalar Laplace–Beltrami operator. In odd complex dimension, these estimates are sharp, in the
Eigenvalue estimates for the Dirac operator on quaternionic Kähler manifolds
Abstract. We consider the Dirac operator on compact quaternionic Kähler manifolds and prove a lower bound for the spectrum. This estimate is sharp since it is the first eigenvalue of the Dirac
...
1
2
3
...