호남수학학술지 (Honam Mathematical Journal)

  • 제46권4호
  • /
  • Pages.587-605
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  • 2024
  • /
  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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THE ZETA-DETERMINANTS OF LAPLACIANS ON THE MOBIUS BAND AND KLEIN BOTTLE

  • Yoonweon Lee (Department of Mathematics Education, Inha University)
  • 투고 : 2024.01.22
  • 심사 : 2024.07.18
  • 발행 : 2024.12.20
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초록

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.

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과제정보

This work was supported by INHA UNIVERSITY Research Grant.

참고문헌

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