Degenerate riemannian structures on certain G-structures

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We consider a Gr-structure defined by a linear operator J and a riemannian metric G. We introduce the compatibility condition JG=0 and obtain a degenerate riemannian structure. We define special bases and linear connections on the structure and obtain a characterization of these connections in terms of J and G. Finally we obtain a characterization of these structures in terms of the holonomy groups of the linear connections.


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This research was carried out under the suggestion and guidance of ProfessorH. A. Eliopoulus of the University of Windsor. The author was supported by a National Research Council of Canada award.

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Closs, M.P. Degenerate riemannian structures on certain G-structures. Annali di Matematica 78, 187–195 (1968) doi:10.1007/BF02415115

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  • Linear Operator
  • Compatibility Condition
  • Special Basis
  • Holonomy Group
  • Linear Connection