On the uniqueness of some differential invariants: d , [ , ] ,

Demeter Krupka; Věra Mikolášová

Czechoslovak Mathematical Journal (1984)

  • Volume: 34, Issue: 4, page 588-597
  • ISSN: 0011-4642

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Krupka, Demeter, and Mikolášová, Věra. "On the uniqueness of some differential invariants: $d$, $[,]$, $\nabla $." Czechoslovak Mathematical Journal 34.4 (1984): 588-597. <http://eudml.org/doc/13482>.

@article{Krupka1984,
author = {Krupka, Demeter, Mikolášová, Věra},
journal = {Czechoslovak Mathematical Journal},
keywords = {natural differential operators; exterior differential; Lie bracket; linear connections},
language = {eng},
number = {4},
pages = {588-597},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the uniqueness of some differential invariants: $d$, $[,]$, $\nabla $},
url = {http://eudml.org/doc/13482},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Krupka, Demeter
AU - Mikolášová, Věra
TI - On the uniqueness of some differential invariants: $d$, $[,]$, $\nabla $
JO - Czechoslovak Mathematical Journal
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 34
IS - 4
SP - 588
EP - 597
LA - eng
KW - natural differential operators; exterior differential; Lie bracket; linear connections
UR - http://eudml.org/doc/13482
ER -

References

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  1. R. L. Bishop R. J. Crittenden, Geometry of Manifolds, Academic Press, New York and London, 1964. (1964) MR0169148
  2. J. A. Dieudonné J. B. Carrel, Invariant Theory, Old and New, Academic Press, New York and London, 1971. (1971) MR0279102
  3. D. B. Epstein, Natural tensors on Riemannian manifolds, J. Differential Geom. 10 (1975), 631-645. (1975) Zbl0321.53039MR0415531
  4. I. Kolář, On the prolongations of geometric object fields, An. Sti. Univ. "Al. I. Cuza'' Iasi, 17 (1971), 437-446. (1971) MR0305278
  5. D. Krupka, Differential Invariants, Lecture Notes, Faculty of Science, Purkyně University, Brno, 1979 (preprint). (1979) 
  6. D. Krupka, Elementary theory of differential invariants, Arch. Math. XIV (1978), 207-214. (1978) Zbl0428.58002MR0512763
  7. D. Krupka, Local invariants of a linear connection, Colloquia Mathematica Societatis Janos Bolyai, 31. Differential Geometry, Budapest (Hungary), 1979, North-Holland, 1982, 349-369. (1979) MR0706930
  8. D. Krupka, Reducibility theorems for differentiable liftings in fiber bundles, Arch. Math. XV (1979) 93-106. (1979) Zbl0439.55009MR0563142
  9. V. Mikolášová, On the functional independence of scalar invariants of curvature for dimensions n = 2, 3, 4, Math. Slovaca 32, 1982, 349-354. (1982) MR0676570
  10. A. Nijenhuis, Natural bundles and their general properties, Differential Geometry, in honour of K. Yano, Kinokunyia, Tokyo, 1972, 317-334. (1972) Zbl0246.53018MR0380862
  11. R. S. Palais, 10.1090/S0002-9947-1959-0116352-7, Trans. Amer. Math. Soc. 92 (1959), 125-141. (1959) Zbl0092.30802MR0116352DOI10.1090/S0002-9947-1959-0116352-7
  12. R. S. Palais C. L. Terng, 10.1016/0040-9383(77)90008-8, Topology 16 (1977), 271 - 277. (1977) MR0467787DOI10.1016/0040-9383(77)90008-8
  13. P. Stredder, Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups, J. Differential Geom. 10 (1975), 647-660. (1975) Zbl0318.53046MR0415692
  14. С. L. Terng, 10.2307/2373910, Amer. J. Math. 100 (1978), 775-828. (1978) Zbl0422.58001MR0509074DOI10.2307/2373910

Citations in EuDML Documents

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  1. Jan Slovák, On natural connections on Riemannian manifolds
  2. Michal Krupka, Anti-holonomic jets and the Lie bracket
  3. Josef Janyška, Remarks on the Nijenhuis tensor and almost complex connections
  4. Dao Qui Chao, Demeter Krupka, 3rd order differential invariants of coframes
  5. Piotr Kobak, The structure tensor and first order natural differential operators
  6. Andreas Čap, All linear and bilinear natural concomitants of vector valued differential forms
  7. Oldřich Kowalski, Masami Sekizawa, Invariance of g -natural metrics on linear frame bundles

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