Remarks on natural differential operators with tensor fields

Josef Janyška

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 5, page 289-308
  • ISSN: 0044-8753

Abstract

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We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations.

How to cite

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Janyška, Josef. "Remarks on natural differential operators with tensor fields." Archivum Mathematicum 055.5 (2019): 289-308. <http://eudml.org/doc/294157>.

@article{Janyška2019,
abstract = {We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations.},
author = {Janyška, Josef},
journal = {Archivum Mathematicum},
keywords = {tensor field; natural differential operator; Lie derivative; Yano-Ako operator},
language = {eng},
number = {5},
pages = {289-308},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Remarks on natural differential operators with tensor fields},
url = {http://eudml.org/doc/294157},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Janyška, Josef
TI - Remarks on natural differential operators with tensor fields
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 5
SP - 289
EP - 308
AB - We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete situations.
LA - eng
KW - tensor field; natural differential operator; Lie derivative; Yano-Ako operator
UR - http://eudml.org/doc/294157
ER -

References

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  2. Frölicher, A., Nijenhuis, A., 10.1016/S1385-7258(56)50047-9, Nederl. Akad. Wetensch. Proc. Ser. A 59 (1956), 338–350, 351–359. (1956) MR0082554DOI10.1016/S1385-7258(56)50047-9
  3. Kolář, I., Michor, P.W., Slovák, J., Natural Operations in Differential Geometry, Springer–Verlag, 1993. (1993) MR1202431
  4. Krupka, D., Janyška, J., Lectures on Differential Invariants, Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno, 1990. (1990) MR1108622
  5. Salimov, A., 10.1007/s00022-010-0059-6, J. Geom. 99 (2010), 107–145, DOI: 10.1007/s00022-010-0059-6. (2010) MR2823104DOI10.1007/s00022-010-0059-6
  6. Schouten, J.A., On the differential operators of first order in tensor calculus, Rapport ZA 1953-012, Math. Centrum Amsterdam (1953), 6 pp. (1953) MR0062508
  7. Schouten, J.A., Ricci-Calculus: An Introduction to Tensor Analysis and Its Geometrical Applications, 2nd ed., Springer–Verlag Berlin, Heidelberg, 1954. (1954) MR0066025
  8. Yano, K., Ako, M., 10.2996/kmj/1138845745, Kodai Math. Sem. Rep. 20 (1968), 414–436. (1968) MR0234370DOI10.2996/kmj/1138845745

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