On metrics and super-Riemann surfaces
type: Item
instance of: scholarly article
title: On metrics and super-Riemann surfaces
zbMATH Open document ID: 0652.58014
DOI: 10.1007/BF00420309
author: Luke Hodgkin
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The author considers a super-Riemann surface M with compact body \(\epsilon\) (M) and shows that for any given metric \(\mu_ 0\) on \(\epsilon\) (M) there is a metric \(\mu\) in M whose body is \(\mu_ 0\) (theorem 1) and that if the genus \((\epsilon (M))>1\) then M admits a unique metric whose lift to the universal cover \(\tilde M\) is superconformally equivalent to the standard metric on the super-half- plane (Baranov-Shvarts metric). This result explains a rather surprising result that the Teichmüller space for arbitrary super-Riemann surface with compact body (obtained by the author in a previous paper) coincides with the one obtained by Crane and Rabin, although they imposed a strong metrizability assumption.
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 4064093
zbMATH Keywords: superconformally equivalent
zbMATH Keywords: super-half-plane
zbMATH Keywords: super-Riemann surface
MaRDI profile type: Publication
cites work: A direct calculation of super-Teichmüller space
cites work: Super Riemann surfaces: Uniformization and Teichmüller theory
cites work: Superspaces and supersymmetries
cites work: Formes différentielles et cohomologie sur une variété analytique complexe
cites work: Q5565313
cites work: Q5547767
cites work: Q5513203
full work available at URL: https://doi.org/10.1007/bf00420309
OpenAlex ID: W1972611451
description: scientific article; zbMATH DE number 4064093