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Dirac Operators on Hermitian Spin Surfaces |
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| Authors: | B. Alexandrov S. Ivanov |
| Affiliation: | (1) Department of Mathematics, University of Sofia !["lsquo"]("/content/g17l4k667x642254/xlarge8216.gif") St. Kl. Ohridski!["rsquo"]("/content/g17l4k667x642254/xlarge8217.gif") , 5 James Bourchier Blvd., 1126 Sofia, Bulgaria. e-mail;(2) Department of Mathematics, University of Sofia St. Kl. Ohridski, 5 James Bourchier Blvd., 1126 Sofia, Bulgaria |
| Abstract: | We prove the conformal invariance of the dimension of thekernel of any of the self-adjoint Dirac operators associated to thecanonical Hermitian connections on Hermitian spin surface. In the caseof a surface of nonnegative conformal scalar curvature we estimate thefirst eigenvalue of the self-adjoint Dirac operator associated to theChern connection and list the surfaces on which its kernel isnontrivial. |
| Keywords: | Dirac operator Hermitian surface |
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