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  • Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between parallel locally direct subsheaves and holonomy-invariant vector supersubspaces are obtained. As the special case, the holonomy of linear connections on supermanifolds is studied. Examples of parallel geometric structures on supermanifolds and the corresponding holonomies are given. For Riemannian supermanifolds an analog of the Wu theorem is proved. Berger superalgebras are defined and their examples are given.
  • Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between parallel locally direct subsheaves and holonomy-invariant vector supersubspaces are obtained. As the special case, the holonomy of linear connections on supermanifolds is studied. Examples of parallel geometric structures on supermanifolds and the corresponding holonomies are given. For Riemannian supermanifolds an analog of the Wu theorem is proved. Berger superalgebras are defined and their examples are given. (en)
Title
  • Holonomy of supermanifolds
  • Holonomy of supermanifolds (en)
skos:prefLabel
  • Holonomy of supermanifolds
  • Holonomy of supermanifolds (en)
skos:notation
  • RIV/00216224:14310/09:00035578!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(LC505)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
  • Galaev, Anton
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 317701
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/09:00035578
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Supermanifold; Superconnection; Holonomy algebra; Berger superalgebra (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [0AE565C46515]
http://linked.open...i/riv/nazevZdroje
  • Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 79/2009
http://linked.open...iv/tvurceVysledku
  • Galaev, Anton
http://linked.open...ain/vavai/riv/wos
  • 000266035600005
issn
  • 0025-5858
number of pages
http://localhost/t...ganizacniJednotka
  • 14310
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