### Abstract

Laplace operators perturbed by meromorphic potential on the Riemann and separated-type Klein surfaces are constructed and their indices are calculated in two different ways. The topological expressions for the indices are obtained from the study of the spectral properties of the operators. Analytical expressions are provided by the heat kernel approach in terms of functional integrals. As a result, two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated-type Klein) surfaces are derived.

Original language | English |
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Pages (from-to) | 249-262 |

Number of pages | 14 |

Journal | Letters in Mathematical Physics |

Volume | 43 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1998 |

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### Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*43*(3), 249-262. https://doi.org/10.1023/A:1007422323346

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*Letters in Mathematical Physics*, vol. 43, no. 3, pp. 249-262. https://doi.org/10.1023/A:1007422323346

**New Index Formulas as a Meromorphic Generalization of the Chern-Gauss-Bonnet Theorem.** / Borisov, N. V.; Illinski, K. N.; Kalinin, G. V.

Research output

TY - JOUR

T1 - New Index Formulas as a Meromorphic Generalization of the Chern-Gauss-Bonnet Theorem

AU - Borisov, N. V.

AU - Illinski, K. N.

AU - Kalinin, G. V.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - Laplace operators perturbed by meromorphic potential on the Riemann and separated-type Klein surfaces are constructed and their indices are calculated in two different ways. The topological expressions for the indices are obtained from the study of the spectral properties of the operators. Analytical expressions are provided by the heat kernel approach in terms of functional integrals. As a result, two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated-type Klein) surfaces are derived.

AB - Laplace operators perturbed by meromorphic potential on the Riemann and separated-type Klein surfaces are constructed and their indices are calculated in two different ways. The topological expressions for the indices are obtained from the study of the spectral properties of the operators. Analytical expressions are provided by the heat kernel approach in terms of functional integrals. As a result, two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated-type Klein) surfaces are derived.

KW - Index

KW - Klein surface

KW - Meromorphic function

KW - Supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=1842685614&partnerID=8YFLogxK

U2 - 10.1023/A:1007422323346

DO - 10.1023/A:1007422323346

M3 - Article

AN - SCOPUS:1842685614

VL - 43

SP - 249

EP - 262

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 3

ER -