Generalised connections over a vector bundle map

Differential Geometry and its Application

Volumn 18, Issue 3, 2003, Pages 295-317

  Cantrijn, Frans ^a   Langerock, Bavo ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Fibre bundles; Generalised connections; Lie algebroids; Pre Lie algebroids

Indexed keywords

EID: 0037404265     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(02)00164-X     Document Type: Article

References (29)

1. Antonelli P.L. Ingarden R.S. Matsumoto M. The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology Fundamental Theories of Physics 58 1993 Kluwer Dordrecht
2. Etayo F. A coordinate-free survey on pseudo-connections Rev. Acad. Canar. Cienc. 5 1993 125-137
3. Falbel E. Gorodski C. Rumin M. Holonomy of sub-Riemannian manifolds Int. J. Math. 8 1997 317-344
4. Fernandes R.L. Connections in Poisson geometry. I: Holonomy and invariants J. Differential Geom. 54 2000 303-366
5. Fernandes R.L. Lie algebroids, holonomy and characteristic classes, Preprint, Dept. of Math., Instituto Superior Técnico, Lisboa, 2000 also: math.DG/0007132.
6. Grabowski J. Urbanski P. Lie algebroids and Poisson-Nijenhuis structures Rep. Math. Phys. 40 1997 195-208
7. Grabowski J. Urbanski P. Algebroids-general differential calculi on vector bundles J. Geom. Phys. 31 1999 111-141
8. nGreub W. Halperin S. Vanstone R. Connections, Curvature, and Cohomology, Vols. I, II and III Pure and Applied Mathematics 47 1972, 1973 Academic Press New York
9. Kamber F. Tondeur P. Foliated Bundles and Characteristic Classes Lecture Notes in Math. 493 1975 Springer Berlin
10. Kobayashi S. Nomizu K. Foundations of Differential Geometry, Vols. 1, 2 Interscience Tracts in Pure and Appl. Math. 1963, 1969 Interscience New York
11. Kolář I. Michor P. Slovák J. Natural Operations in Differential Geometry 1993 Springer Berlin
12. Kosmann-Schwarzbach Y. Magri F. Poisson-Nijenhuis structures Ann. Inst. Henri Poincaré, Phys. Théor. 53 1990 35-81
13. Kubarski J. Bott's vanishing theorem for regular Lie algebroids Trans. Amer. Math. Soc. 348 1996 2151-2167
14. B. Langerock, A connection theoretic approach to sub-Riemannian geometry, J. Geom. Phys., to be published
15. Langerock B. Nonholonomic mechanics and connections over a bundle map J. Phys. A 34 2001 L609-L615
16. Mackenzie K. Lie Groupoids and Lie Algebroids in Differential Geometry London Math. Soc. Lecture Notes Series 124 1987 Cambridge Univ. Press Cambridge
17. Mangiarotti L. Sardanashvily G. Connections in Classical and Quantum Field Theory 2000 World Scientific Singapore
18. M. Popescu, P. Popescu, Geometric objects defined by almost Lie structures, Preprint, Dept. of Math., University of Craiova (Romania), 2001
19. Popescu P. On the geometry of relative tangent spaces Rev. Roum. Math. Pures Appl. 37 1992 727-733
20. Saunders D. The Geometry of Jet Bundles London Math. Soc. Lecture Notes Series 142 1989 Cambridge Univ. Press Cambridge
21. Sharpe R.W. Differential Geometry. Cartan's Generalization of Klein's Erlangen Program Graduate Texts in Math. 166 1997 Springer Berlin
22. Strichartz R. Sub-Riemannian geometry J. Differential Geom. 24 1986 221-263
23. Strichartz R. Corrections to "Sub-Riemannian Geometry" J. Differential Geom. 30 1989 595-596
24. Sussmann H. Orbits of families of vector fields and integrability of distributions Trans. Amer. Math. Soc. 180 1973 171-188
25. Vaisman I. On the geometric quantization of Poisson manifolds J. Math. Phys. 32 1991 3339-3345
26. Vaisman I. Lectures on the Geometry of Poisson Manifolds Progress in Math. 118 1994 Birkhäuser Basel
27. Vilms J. Connections on tangent bundles J. Differential Geom. 1 1967 235-243
28. Wong Y.C. Linear connections and quasi connections on a differentiable manifold Tôhuku Math. J. 14 1962 48-63
29. Yano K. Ishihara S. Tangent and Cotangent Bundles 1973 Marcel Dekker New York