liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A noncommutative catenoid
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8727-2169
Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
2018 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 108, no 7, p. 1601-1622Article in journal (Refereed) Published
Abstract [en]

A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

Place, publisher, year, edition, pages
Springer Netherlands, 2018. Vol. 108, no 7, p. 1601-1622
Keywords [en]
Noncommutative catenoid; Noncommutative Riemannian geometry; Noncommutative minimal surface; Noncommutative curvature
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-148078DOI: 10.1007/s11005-017-1042-zISI: 000432328500002PubMedID: 29780201Scopus ID: 2-s2.0-85040035304OAI: oai:DiVA.org:liu-148078DiVA, id: diva2:1211372
Note

Funding Agencies|Swedish Research Council; EU COST action QSPACE

Available from: 2018-05-30 Created: 2018-05-30 Last updated: 2018-06-26Bibliographically approved

Open Access in DiVA

fulltext(472 kB)63 downloads
File information
File name FULLTEXT01.pdfFile size 472 kBChecksum SHA-512
b46b30152412df36c52e40cbc3be8ca4c203cb550dc0421098d576088b5c9231e781b6450b36aed398fce5cbb0f8e83fff89a8b866e6a45d16b3e35b83dadc0b
Type fulltextMimetype application/pdf

Other links

Publisher's full textPubMedScopus

Search in DiVA

By author/editor
Arnlind, JoakimHolm, Christoffer
By organisation
Mathematics and Applied MathematicsFaculty of Science & EngineeringDepartment of Mathematics
In the same journal
Letters in Mathematical Physics
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 63 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
pubmed
urn-nbn

Altmetric score

doi
pubmed
urn-nbn
Total: 311 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf