On the Spectrum of geometric operators on Kähler manifolds - Mathematics > Differential GeometryReport as inadecuate




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Abstract: On a compact K\-ahler manifold there is a canonical action of aLie-superalgebra on the space of differential forms. It is generated by thedifferentials, the Lefschetz operator and the adjoints of these operators. Wedetermine the asymptotic distribution of irreducible representations of thisLie-superalgebra on the eigenspaces of the Laplace-Beltrami operator. Becauseof the high degree of symmetry the Laplace-Beltrami operator on forms can notbe quantum ergodic. We show that after taking these symmetries into accountquantum ergodicity holds for the Laplace-Beltrami operator and for theSpin^c-Dirac operators if the unitary frame flow is ergodic. The assumptionsfor our theorem are known to be satisfied for instance for negatively curvedK\-ahler manifolds of odd complex dimension.



Author: Dmitry Jakobson, Alexander Strohmaier, Steve Zelditch

Source: https://arxiv.org/







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