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Sfb288 logo Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 604


Hermitian spin surfaces with small eigenvalues of the Dolbeault operator.

Bogdan Alexandrov

We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf surface. We give a complete classification of the ruled surfaces with this property. For the Hopf surfaces we obtain a partial classification and some examples.


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