Hermitian spin surfaces with small eigenvalues of the Dolbeault operator
Differential Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0403074,
title = {Hermitian spin surfaces with small eigenvalues of the Dolbeault operator},
author = {Bogdan Alexandrov},
journal= {arXiv preprint arXiv:math/0403074},
year = {2007}
}
Comments
13 pages