On lifts of symplectic vector bundles and connections to Weil bundles

Authors

  • E. Hinamari Mang-massou Department of Mathematics and Computer Science, Faculty of Science University of Ngaoundéré, PO.BOX 454, Ngaoundéré, Cameroon
  • A. Ntyam Department of Mathematics, Higher Teacher Training College University of Yaoundé 1, PO.BOX 47 Yaoundé, Cameroon

DOI:

https://doi.org/10.17398/

Keywords:

Symplectic vector bundle, differential form, connection, Weil functor, lift

Abstract

In this paper, we generalize to Frobenius-Weil bundles some lifts of symplectic manifolds and symplectic vector bundles.

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References

L.A. Cordero, C.T.J. Dodson, M. de León, “Differential geometry of frame bundles”, Kluwer Academic Publishers, Dordrecht, 1989.

M. Doupovec, Natural transformations of the composition of Weil and cotangent functors, Ann. Polon. Math. 77 (2) (2001), 105 – 117.

M. Doupovec, M. Kureš, Some geometric constructions on Frobenius Weil bundles, Differential Geom. Appl. 35 (2014), 143 – 149.

J. Gancarzewicz, W.M. Mikulski, Z. Pogoda, Lifts of some tensor fields and connections to product preserving functors, Nagoya Math. J. 135 (1994), 1 – 14.

K. Grabowska, J. Grabowski, Z. Ravanpak, VB-structures and generalizations, Ann. Global Anal. Geom. Volume 62 (2022), 235 – 284.

K. Konieczna, P. Urbański, Double vector bundles and duality, Arch. Math. (Brno) 35 (1999), 59 – 95.

I. Kolář, On the natural operators on vector fields, Ann. Global Anal. Geom. 6 (1988), 109 – 117.

I. Kolář, P.W. Michor, J. Slovák, “Natural operations in differential geometry”, Springer-Verlag, Berlin, 1993.

P.M. Kouotchop Wamba, G.F. Wankap Nono, A. Ntyam, Prolongations of G-structures related to Weil bundles and some applications, Extracta Math. 37 (1) (2022), 111 – 138.

Y. Kosmann-Schwarzbach, Multiplicativity, from Lie groups to generalized geometry, in “Geometry of jets and fields”, Banach Center Publ., 110, Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2016, 131 – 166.

J. Kurek, W.M. Mikulski, Symplectic structures on the tangent bundles of symplectic and cosymplectic manifolds, Ann. Polon. Math. 82 (3) (2003), 273 – 285.

J. Kurek, W.M. Mikulski, Canonical symplectic structures on the rth order tangent bundle of a symplectic manifold, Extracta Math. 21 (2) (2006), 159 – 166.

K.C.H. Mackenzie, “General theory of Lie groupoids and Lie algebroids”, London Math. Soc. Lecture Note Ser., 213, Cambridge University Press, Cambridge, 2005.

D. McDuff, D. Salamon, “Introduction to symplectic topology”, 2nd edition, Oxford Math. Monogr., Oxford University Press, New York, 1998.

A. Ntyam, J.W. Kamga, New versions of curvature and torsion formulas for the complete lifting of a linear connection to Weil bundles, Ann. Polon. Math. 82 (3) (2003), 233 – 240.

E. Okassa, Relèvements des structures symplectiques et pseudo-Riemanniennes à des variétés de points proches, Nagoya Math. 115 (1989), 63 – 71.

J. Slovák, Prolongations of connections and sprays with respect to Weil functors, Rend. Circ. Mat. Palermo (2) Suppl. (14) (1987), 143 – 155.

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Published

2024-05-07

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Section

Articles in press

How to Cite

On lifts of symplectic vector bundles and connections to Weil bundles. (2024). Extracta Mathematicae. https://doi.org/10.17398/

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