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  • The purpose of this project is to study holonomy of Riemannian supermanifolds following two main reasons: There is a deep theory of holonomy of Riemannian smooth manifolds and various applications of these results in theoretical physics. At the same time, supermanifolds were obtained by physicists when introducing supersymmetry, and during their quest for a unified field theory of elementary particles and the fundamental force. I introduced the concept of holonomy of supermanifolds recently and have begun its study. The aim of the project is to solve the following problems: to get a classification of holonomy algebras of some classes of Riemannian supermanifolds, to describe the geometries of the corresponding supermanifolds, to get constructions of supermanifolds with special holonomies and to find applications to connections on usual vector bundles, as they give rise to connections on supermanifolds. These results can be used by theoretical physicists, e.g. in supersymmetry and superstrings theory. (en)
  • Cílem projektu je řešit tyto problémy: klasifikace algeber holonomií vhodných tříd supervariet, charakterizace geometrií příslušných supervariet, konstrukce supervariet se speciálními holonomiemi a využití těchto holonomií ve studiu konexí na vektorových bandlech. (cs)
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  • Holonomy of Riemannian supermanifolds and related geometric structures (en)
  • Holonomie Riemannových supervariet a související geometrické struktury (cs)
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  • Riemannova supervarieta; algebra holonomií; Bergerova superalgebra; paralelní objekty (en)
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