# Principal prolongations and geometries modeled on homogeneous spaces

Archivum Mathematicum (1996)

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

## Access Full Article

top## Abstract

top## How to cite

topSlovák, 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- Differential geometry of Cartan connections, ESI Preprint 39, Publ. Math. Debrecen 47 (1995), 349–375. (1995) MR1362298
- Almost Hermitian symmetric manifolds, I: Local twistor theory;, Duke Math. J. 63 (1991), 81–111. (1991) Zbl0724.53019MR1106939
- [unknown], paper in preparation.
- On local flatness of AHS–manifolds, to appear in Rendiconti Circ. Mat. Palermo, Proceedings of the Winter School Geometry and Physics, Srní1995.
- 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
- 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
- Transformation groups in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1972. (1972) Zbl0246.53031MR0355886
- Canonical forms on the prolongations of principal fiber bundles, Rev. Roumaine Math. Pures Appl. 16 (1971), 1091–1106. (1971) MR0301668
- Higher order torsions of spaces with Cartan Connection, Cahiers Topologie Géom. Différentielle 12 (1971), 137–146. (1971) MR0315619
- Generalized $G$-structures and $G$-structures of higher order, Bollettino U. M. Ital. 12, Suppl. 3 (1975), 245–256. (1975) MR0445424
- A generalization of the torsion form, Časopis pro pěstování matematiky 100 (1975), 284–290. (1975) MR0383287
- Natural operations in differential geometry, Springer-Verlag, Berlin Heidelberg New York, 1993. (1993) MR1202431
- The Convenient Setting for Global Analysis, to appear, Surveys and Monographs, AMS, Providence, 1997. (1997) MR1471480
- 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
- Geometric structures on filtered manifolds, Hokkaido Math. J. 22 (1993), 263–347. (1993) Zbl0801.53019MR1245130
- 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) MR1396607
- On differential systems, graded Lie algebras and pseudo-groups, J. Math. Kyoto Univ. 10 (1970), 1–82. (1970) Zbl0206.50503MR0266258
- On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japanese J. Math. 2 (1976), 131–190. (1976) Zbl0346.32010MR0589931
- On the equivalence problems associated with simple graded Lie algebras, Hokkaido Math. J. 8 (1979), 23–84. (1979) Zbl0409.17013MR0533089

## NotesEmbed ?

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