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  • The trace decomposition problem may be considered as a finding of an expression of given tensor as a summ of a certain traceless tensor and linear combination of tensors of certain type. The solution on this problem is well known in the case of tensors on real vector spaces with metric tensor, when independent elements of the mentioned linear combinations are Kronecker delta-tensors. This case may be considered as belonging to the representation theory of the orthogonal group. This decomposition problem may be naturally generalized for F-traceless case. The solution of this case is used for the study of geodesic and holomorphically projective mappings of certain Riemannian spaces, especially. We bring the explicit decomposition formulas for tensors of the type (1,1), (1,2) and - for special condition - (1,3). Further, decompositions for the type (2,2) and (1,3) are given for tensor spaces with almost complex structure.
  • The trace decomposition problem may be considered as a finding of an expression of given tensor as a summ of a certain traceless tensor and linear combination of tensors of certain type. The solution on this problem is well known in the case of tensors on real vector spaces with metric tensor, when independent elements of the mentioned linear combinations are Kronecker delta-tensors. This case may be considered as belonging to the representation theory of the orthogonal group. This decomposition problem may be naturally generalized for F-traceless case. The solution of this case is used for the study of geodesic and holomorphically projective mappings of certain Riemannian spaces, especially. We bring the explicit decomposition formulas for tensors of the type (1,1), (1,2) and - for special condition - (1,3). Further, decompositions for the type (2,2) and (1,3) are given for tensor spaces with almost complex structure. (en)
Title
  • On F-traceless decomposition problem
  • On F-traceless decomposition problem (en)
skos:prefLabel
  • On F-traceless decomposition problem
  • On F-traceless decomposition problem (en)
skos:notation
  • RIV/61989592:15310/11:33116851!RIV12-MSM-15310___
http://linked.open...avai/riv/aktivita
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  • S
http://linked.open...vai/riv/dodaniDat
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  • 218024
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  • RIV/61989592:15310/11:33116851
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  • Tensor, decomposition problem, traceless, F-tracelles, Riemannian space, Kahlerian space (en)
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http://linked.open...ontrolniKodProRIV
  • [471DB4B34D4B]
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  • Brno
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  • Brno
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  • Proceedings of Contributions of 7th Conference on Mathematics and Physics on Technical Universities
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  • Jukl, Marek
  • Juklová, Lenka
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
number of pages
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  • Univerzita obrany
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  • 978-80-7231-818-6
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  • 15310
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