The structure tensor and first order natural differential operators

Piotr Kobak

Archivum Mathematicum (1992)

  • Volume: 028, Issue: 3-4, page 121-138
  • ISSN: 0044-8753

Abstract

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The notion of a structure tensor of section of first order natural bundles with homogeneous standard fibre is introduced. Properties of the structure tensor operator are studied. The universal factorization property of the structure tensor operator is proved and used for classification of first order * -natural differential operators D ̲ : T × T ̲ → T ̲ for n ≥ 3 .

How to cite

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Kobak, Piotr. "The structure tensor and first order natural differential operators." Archivum Mathematicum 028.3-4 (1992): 121-138. <http://eudml.org/doc/247346>.

@article{Kobak1992,
abstract = {The notion of a structure tensor of section of first order natural bundles with homogeneous standard fibre is introduced. Properties of the structure tensor operator are studied. The universal factorization property of the structure tensor operator is proved and used for classification of first order $*$-natural differential operators $\underline\{D\}:\underline\{T\times T\} \rightarrow \underline\{T\}$ for $n\ge 3$.},
author = {Kobak, Piotr},
journal = {Archivum Mathematicum},
keywords = {natural bundle; natural affine; vector bundle; natural differential operator; G-structure; structure tensor; structure tensor; -structure; first order natural bundle},
language = {eng},
number = {3-4},
pages = {121-138},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The structure tensor and first order natural differential operators},
url = {http://eudml.org/doc/247346},
volume = {028},
year = {1992},
}

TY - JOUR
AU - Kobak, Piotr
TI - The structure tensor and first order natural differential operators
JO - Archivum Mathematicum
PY - 1992
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 028
IS - 3-4
SP - 121
EP - 138
AB - The notion of a structure tensor of section of first order natural bundles with homogeneous standard fibre is introduced. Properties of the structure tensor operator are studied. The universal factorization property of the structure tensor operator is proved and used for classification of first order $*$-natural differential operators $\underline{D}:\underline{T\times T} \rightarrow \underline{T}$ for $n\ge 3$.
LA - eng
KW - natural bundle; natural affine; vector bundle; natural differential operator; G-structure; structure tensor; structure tensor; -structure; first order natural bundle
UR - http://eudml.org/doc/247346
ER -

References

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  1. Sur la gèometrie differèntiele des G -structures, Ann. Inst. Fourier 10 (1960). (1960) MR0126800
  2. Natural tensors on Riemannian manifolds, J. Diff. Geom. 10 (1975), 631 -645. (1975) Zbl0321.53039MR0415531
  3. Theory of G -structures, Publications of the Study Group of Geometry 1 (1972), Okayama. (1972) Zbl0235.53035MR0348664
  4. Liftings of functions and vector fields to natural bundles, Diss. Math. CCXII (1983), Institute of Mathematics, Warszawa. (1983) MR0697471
  5. All natural concomitants of vector valued differential forms, Proc. of the Winter School of Geometry and Physics (1987), Srní. (1987) MR0946715
  6. Natural Lagrangian structures, Diff. Geom. 12 (1984), Banach center Publications, PWN - Polish Scientific Publisher, Warszaw, 185-210. (1984) Zbl0572.58007MR0961080
  7. On the uniqueness of some differential invariants: d , [ , ] , ▿ , Cz. Math. J. 34(109) (1984), 588-597. (1984) MR0764440
  8. Fibre bundles associated with fields of geometric objects and a structure tensor, preprint, International Centre For Theoretical Physics, Miramare, Trieste, 1987. 
  9. On the reduction Theorems, Ann. Polon. Math. XXVI (1972), 125-133. (1972) MR0307078
  10. Systems of partial differential equations and Lie pseudogroups, Gordon and Breach, 1978. (1978) Zbl0418.35028MR0517402
  11. Natural vector bundle and natural differential operators, Am. J. Math. 100 (1978), 775-828. (1978) MR0509074
  12. Foundations of differential geometry of natural bundles, Univ. of Caracas, 1984. (1984) 

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