### Abstract

Special properties of realizations of supersymmetry on noncompact manifolds are discussed. On the basis of the supersymrnetric scattering theory and the supersymmetric trace formulas, the absolute or relative Euler characteristic of a barrier in R^{N} can be obtained from the scattering data for the Laplace operator on forms with absolute or relative boundary conditions. An analog of the Chern-Gauss-Bonnet theorem for noncompact manifolds is also obtained. The map from the stationary curve of an antiholomorphic involution on a compact Riemann surface to the real circle on the Riemann sphere, generated by a real meromorphic function is considered. An analytic expression for its topological index is obtained by using supersymmetric quantum mechanics with meromorphic superpotential on the klein surface.

Original language | English |
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Pages (from-to) | 1605-1618 |

Number of pages | 14 |

Journal | Journal of Mathematical Sciences |

Volume | 85 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 1997 |

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### Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Applied Mathematics

### Cite this

*Journal of Mathematical Sciences*,

*85*(1), 1605-1618. https://doi.org/10.1007/BF02355321

}

*Journal of Mathematical Sciences*, vol. 85, no. 1, pp. 1605-1618. https://doi.org/10.1007/BF02355321

**Supersymmetry on noncompact manifolds and complex geometry.** / Borisov, N. V.; Il'inskii, K. N.

Research output

TY - JOUR

T1 - Supersymmetry on noncompact manifolds and complex geometry

AU - Borisov, N. V.

AU - Il'inskii, K. N.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Special properties of realizations of supersymmetry on noncompact manifolds are discussed. On the basis of the supersymrnetric scattering theory and the supersymmetric trace formulas, the absolute or relative Euler characteristic of a barrier in RN can be obtained from the scattering data for the Laplace operator on forms with absolute or relative boundary conditions. An analog of the Chern-Gauss-Bonnet theorem for noncompact manifolds is also obtained. The map from the stationary curve of an antiholomorphic involution on a compact Riemann surface to the real circle on the Riemann sphere, generated by a real meromorphic function is considered. An analytic expression for its topological index is obtained by using supersymmetric quantum mechanics with meromorphic superpotential on the klein surface.

AB - Special properties of realizations of supersymmetry on noncompact manifolds are discussed. On the basis of the supersymrnetric scattering theory and the supersymmetric trace formulas, the absolute or relative Euler characteristic of a barrier in RN can be obtained from the scattering data for the Laplace operator on forms with absolute or relative boundary conditions. An analog of the Chern-Gauss-Bonnet theorem for noncompact manifolds is also obtained. The map from the stationary curve of an antiholomorphic involution on a compact Riemann surface to the real circle on the Riemann sphere, generated by a real meromorphic function is considered. An analytic expression for its topological index is obtained by using supersymmetric quantum mechanics with meromorphic superpotential on the klein surface.

UR - http://www.scopus.com/inward/record.url?scp=53249125066&partnerID=8YFLogxK

U2 - 10.1007/BF02355321

DO - 10.1007/BF02355321

M3 - Article

AN - SCOPUS:53249125066

VL - 85

SP - 1605

EP - 1618

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -