THE ZETA-DETERMINANTS OF LAPLACIANS ON THE MOBIUS BAND AND KLEIN BOTTLE

초록

We compute the zeta-determinants of the scalar Laplacians defined on the Mo<spacing diaeresis>bius band and Klein bottle when the flat metrics are given. We consider the difference between these zeta-determinants and those of the product manifolds, and use the BFK-gluing formula to compute the difference. The zeta-determinants of product manifolds are well known and this computes the zeta-determinants on the Mo<spacing diaeresis>bius band and Klein bottle. We finally show that the zeta-determinant on the Klein bottle satisfies the BFK-gluing formula.

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