Principal prolongations and geometries modeled on homogeneous spaces

Jan Slovák

Archivum Mathematicum (1996)

  • Volume: 032, Issue: 4, page 325-342
  • ISSN: 0044-8753

Abstract

top
We discuss frame bundles and canonical forms for geometries modeled on homogeneous spaces. Our aim is to introduce a geometric picture based on the non-holonomic jet bundles and principal prolongations as introduced in [Kolář, 71]. The paper has a partly expository character and we focus on very general aspects only. In the final section, various links to known results on the parabolic geometries are given briefly and some directions for further investigations are roughly indicated.

How to cite

top

Slovák, Jan. "Principal prolongations and geometries modeled on homogeneous spaces." Archivum Mathematicum 032.4 (1996): 325-342. <http://eudml.org/doc/18474>.

@article{Slovák1996,
abstract = {We discuss frame bundles and canonical forms for geometries modeled on homogeneous spaces. Our aim is to introduce a geometric picture based on the non-holonomic jet bundles and principal prolongations as introduced in [Kolář, 71]. The paper has a partly expository character and we focus on very general aspects only. In the final section, various links to known results on the parabolic geometries are given briefly and some directions for further investigations are roughly indicated.},
author = {Slovák, Jan},
journal = {Archivum Mathematicum},
keywords = {jet prolongation; principal prolongation; Cartan connection; jet prolongation; principal prolongation; Cartan connection},
language = {eng},
number = {4},
pages = {325-342},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Principal prolongations and geometries modeled on homogeneous spaces},
url = {http://eudml.org/doc/18474},
volume = {032},
year = {1996},
}

TY - JOUR
AU - Slovák, Jan
TI - Principal prolongations and geometries modeled on homogeneous spaces
JO - Archivum Mathematicum
PY - 1996
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 032
IS - 4
SP - 325
EP - 342
AB - We discuss frame bundles and canonical forms for geometries modeled on homogeneous spaces. Our aim is to introduce a geometric picture based on the non-holonomic jet bundles and principal prolongations as introduced in [Kolář, 71]. The paper has a partly expository character and we focus on very general aspects only. In the final section, various links to known results on the parabolic geometries are given briefly and some directions for further investigations are roughly indicated.
LA - eng
KW - jet prolongation; principal prolongation; Cartan connection; jet prolongation; principal prolongation; Cartan connection
UR - http://eudml.org/doc/18474
ER -

References

top
  1. Differential geometry of Cartan connections, ESI Preprint 39, Publ. Math. Debrecen 47 (1995), 349–375. (1995) Zbl0857.53011MR1362298
  2. Almost Hermitian symmetric manifolds, I: Local twistor theory;, Duke Math. J. 63 (1991), 81–111. (1991) Zbl0724.53019MR1106939
  3. [unknown], paper in preparation. 
  4. On local flatness of AHS–manifolds, to appear in Rendiconti Circ. Mat. Palermo, Proceedings of the Winter School Geometry and Physics, Srní1995. Zbl1067.53501
  5. Invariant Operators on Manifolds with Almost Hermitian Symmetric Structures, I. Invariant Differentiation, electronically available at ftp.esi.ac.at, Preprint ESI 186 (1994), 31 pp. (1994) MR1474550
  6. Invariant Operators on Manifolds with Almost Hermitian Symmetric Structures, II. Normal Cartan connections, electronically available at ftp.esi.ac.at, Preprint ESI 194 (1995), 16 pp. (1995) MR1620484
  7. Transformation groups in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1972. (1972) Zbl0246.53031MR0355886
  8. Canonical forms on the prolongations of principal fiber bundles, Rev. Roumaine Math. Pures Appl. 16 (1971), 1091–1106. (1971) MR0301668
  9. Higher order torsions of spaces with Cartan Connection, Cahiers Topologie Géom. Différentielle 12 (1971), 137–146. (1971) Zbl0221.53039MR0315619
  10. Generalized G -structures and G -structures of higher order, Bollettino U. M. Ital. 12, Suppl. 3 (1975), 245–256. (1975) MR0445424
  11. A generalization of the torsion form, Časopis pro pěstování matematiky 100 (1975), 284–290. (1975) MR0383287
  12. Natural operations in differential geometry, Springer-Verlag, Berlin Heidelberg New York, 1993. (1993) Zbl0782.53013MR1202431
  13. The Convenient Setting for Global Analysis, to appear, Surveys and Monographs, AMS, Providence, 1997. (1997) Zbl0889.58001MR1471480
  14. Sur les prolongements des fibrés principaux et des groupoides différentiables banachiques, Analyse global, Sém. Mat. Supérieures, No. 42 (Été, 1969) (1971), 7–108. (1971) Zbl0248.53031MR0356117
  15. Geometric structures on filtered manifolds, Hokkaido Math. J. 22 (1993), 263–347. (1993) Zbl0801.53019MR1245130
  16. The principal prolongation of first order G -structures, Proceedings of the Winter School Geometry and Physics, Srní 1994, Supplemento ai Rendiconti Circ. Mat. Palermo 39 (1996), 123–131. (1996) Zbl0863.53020MR1396607
  17. On differential systems, graded Lie algebras and pseudo-groups, J. Math. Kyoto Univ. 10 (1970), 1–82. (1970) Zbl0206.50503MR0266258
  18. On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japanese J. Math. 2 (1976), 131–190. (1976) Zbl0346.32010MR0589931
  19. On the equivalence problems associated with simple graded Lie algebras, Hokkaido Math. J. 8 (1979), 23–84. (1979) Zbl0409.17013MR0533089

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.