https://www.mdu.se/

mdu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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
The Penrose transform in split signature
Inst Res Fundamental Sci IPM, POB 19395-5746, Tehran, Iran. (MAM)ORCID iD: 0000-0002-4471-1483
2012 (English)In: Differential geometry and its applications (Print), ISSN 0926-2245, E-ISSN 1872-6984, Vol. 30, no 4, p. 334-346Article in journal (Refereed) Published
Abstract [en]

A version of the Penrose transform is introduced in split signature. It relates cohomological data on CP3 \ RP3 and the kernel of differential operators on M, the (real) Grassmannian of 2-planes in R-4. As an example we derive the following cohomological interpretation of the so-called X-ray transform

H-c(1)(CP3\RP3, O(-2)) ->congruent to ker(rectangle(2.2) : Gamma(omega) (M, (epsilon|-1|) over tilde) -> Gamma(omega) (M, (epsilon|-3|) over tilde))

where Gamma(omega) (M, (epsilon|-1|) over tilde) and Gamma(omega) (M, (epsilon|-3|) over tilde) are real analytic sections of certain (homogeneous) line bundles on M, c stands for cohomology with compact support and rectangle(2.2) is the ultrahyperbolic operator. Furthermore, this gives a cohomological realization of the so-called "minimal" representation of SL(4, R). We also present the split Penrose transform in split instanton backgrounds.

Place, publisher, year, edition, pages
2012. Vol. 30, no 4, p. 334-346
Keywords [en]
Penrose transform, Split signature
National Category
Geometry
Identifiers
URN: urn:nbn:se:mdh:diva-60023DOI: 10.1016/j.difgeo.2012.04.005ISI: 000305874500004Scopus ID: 2-s2.0-84860680845OAI: oai:DiVA.org:mdh-60023DiVA, id: diva2:1699153
Available from: 2022-09-27 Created: 2022-09-27 Last updated: 2022-11-17Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records

Aryapoor, Masood

Search in DiVA

By author/editor
Aryapoor, Masood
In the same journal
Differential geometry and its applications (Print)
Geometry

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 79 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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