Connections induced by -tensor fields on cotangent bundles

Anton Dekrét

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 3, page 317-331
  • ISSN: 0862-7959

Abstract

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On cotangent bundles the Liouville field, the Liouville 1-form and the canonical symplectic structure d exist. In this paper interactions between these objects and -tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.

How to cite

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Dekrét, Anton. "Connections induced by $(1,1)$-tensor fields on cotangent bundles." Mathematica Bohemica 123.3 (1998): 317-331. <http://eudml.org/doc/248298>.

@article{Dekrét1998,
abstract = {On cotangent bundles the Liouville field, the Liouville 1-form $\varepsilon $ and the canonical symplectic structure d$\varepsilon $ exist. In this paper interactions between these objects and $\{(1,1)\}$-tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.},
author = {Dekrét, Anton},
journal = {Mathematica Bohemica},
keywords = {connection; almost complex structure; tensor field; Liouville field; canonical symplectic structure; connection; almost complex structure; tensor field; Liouville field; canonical symplectic structure},
language = {eng},
number = {3},
pages = {317-331},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Connections induced by $(1,1)$-tensor fields on cotangent bundles},
url = {http://eudml.org/doc/248298},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Dekrét, Anton
TI - Connections induced by $(1,1)$-tensor fields on cotangent bundles
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 3
SP - 317
EP - 331
AB - On cotangent bundles the Liouville field, the Liouville 1-form $\varepsilon $ and the canonical symplectic structure d$\varepsilon $ exist. In this paper interactions between these objects and ${(1,1)}$-tensor fields on cotangent bundles are studied. Properties of the connections induced by the above structures are investigated.
LA - eng
KW - connection; almost complex structure; tensor field; Liouville field; canonical symplectic structure; connection; almost complex structure; tensor field; Liouville field; canonical symplectic structure
UR - http://eudml.org/doc/248298
ER -

References

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  2. Dekrét A., On almost complex structures on fibre bundles, Acta Univ. M. Belii Math. 3 (1995), 3-8. (1995) Zbl0856.53026MR1409884
  3. Doupovec M., Kurek J., Liftings of tensor fields to the cotangent bundle, Proc. Conf. Diff. Geometry Brno 1995. Masaryk University, Brno, 1996, p. 141-150. (1995) MR1406334
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  5. Klein J., On variational second order differential equations Polynomial case, Proc. Conf. Diff. Geometry and its Applications 1992. Silesian University, Opava, 1993, p. 449-459. (1992) MR1255561
  6. Kolář I., Michor P. W., Slovák J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. (1993) MR1202431
  7. Yano K., Differential Geometry on Complex and Almost Complex Spaces, Pergamon Press, New York, 1965. (1965) Zbl0127.12405MR0187181
  8. Yano K., Ishihara S., Tangent and Cotangent Bundles, M. Dekker Inc., New York, 1973. (1973) Zbl0262.53024MR0350650

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