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

N. V. Borisov, K. N. Illinski, G. V. Kalinin

Research output

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)249-262
Number of pages14
JournalLetters in Mathematical Physics
Volume43
Issue number3
DOIs
Publication statusPublished - 1 Jan 1998

Fingerprint

Klein Surface
Meromorphic
Gauss
theorems
meromorphic functions
Laplace transformation
Functional Integral
Heat Kernel
Laplace Operator
Topological Properties
Meromorphic Function
Spectral Properties
Theorem
operators
heat
Operator
Generalization

Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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

In: Letters in Mathematical Physics, Vol. 43, No. 3, 01.01.1998, p. 249-262.

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

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U2 - 10.1023/A:1007422323346

DO - 10.1023/A:1007422323346

M3 - Article

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

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ER -