Honam Mathematical Journal (호남수학학술지)

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

  • Yoonweon Lee (Department of Mathematics Education, Inha University)
  • Received : 2024.01.22
  • Accepted : 2024.07.18
  • Published : 2024.12.20
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Abstract

We compute the zeta-determinants of the scalar Laplacians defined on the Möbius 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 Möbius band and Klein bottle. We finally show that the zeta-determinant on the Klein bottle satisfies the BFK-gluing formula.

Keywords

Acknowledgement

This work was supported by INHA UNIVERSITY Research Grant.

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