Some framed f -structures on transversally Finsler foliations

Cristian Ida

Annales UMCS, Mathematica (2011)

  • Volume: 65, Issue: 1, page 87-96
  • ISSN: 2083-7402

Abstract

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Some problems concerning to Liouville distribution and framed f-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)-structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

How to cite

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Cristian Ida. " Some framed f -structures on transversally Finsler foliations ." Annales UMCS, Mathematica 65.1 (2011): 87-96. <http://eudml.org/doc/267568>.

@article{CristianIda2011,
abstract = {Some problems concerning to Liouville distribution and framed f-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)-structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.},
author = {Cristian Ida},
journal = {Annales UMCS, Mathematica},
keywords = {Transversally Finsler foliation; Liouville distribution; framed f-structures; transversal Finsler foliation; framed -structure},
language = {eng},
number = {1},
pages = {87-96},
title = { Some framed f -structures on transversally Finsler foliations },
url = {http://eudml.org/doc/267568},
volume = {65},
year = {2011},
}

TY - JOUR
AU - Cristian Ida
TI - Some framed f -structures on transversally Finsler foliations
JO - Annales UMCS, Mathematica
PY - 2011
VL - 65
IS - 1
SP - 87
EP - 96
AB - Some problems concerning to Liouville distribution and framed f-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)-structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.
LA - eng
KW - Transversally Finsler foliation; Liouville distribution; framed f-structures; transversal Finsler foliation; framed -structure
UR - http://eudml.org/doc/267568
ER -

References

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  1. Abate, M., Patrizio, G., Finsler Metrics - A Global Approach, Lecture Notes in Math., 1591, Springer-Verlag, Berlin, 1994. Zbl0837.53001
  2. Anastasiei, M., A framed f-structure on tangent bundle of a Finsler space, An. Univ. Bucureşti, Mat.-Inf., 49 (2000), 3-9. 
  3. Bao, D., Chern, S. S. and Shen, Z., An Introduction to Riemannian Finsler Geometry, Graduate Texts in Math., 200, Springer-Verlag, New York, 2000. 
  4. Bejancu, A., Farran, H. R., On the vertical bundle of a pseudo-Finsler manifold, Int. J. Math. Math. Sci. 22 (3) (1997), 637-642. Zbl0978.53050
  5. Gîrţu, M., An almost paracontact structure on the indicatrix bundle of a Finsler space, Balkan J. Geom. Appl. 7(2) (2002), 43-48. Zbl1026.53043
  6. Gîrţu, M., A framed f(3, -1)-structure on the tangent bundle of a Lagrange space, Demonstratio Math. 37(4) (2004), 955-961. Zbl1076.53094
  7. Hasegawa, I., Yamaguchi, K. and Shimada, H., Sasakian structures on Finsler manifolds, Antonelli, P. L., Miron R. (eds.), Lagrange and Finsler Geometry, Kluwer Acad. Publ., Dordrecht, 1996, 75-80. Zbl0843.53016
  8. Miernowski, A., A note on transversally Finsler foliations, Ann. Univ. Mariae Curie-Skłodowska Sect. A 60 (2006), 57-64. Zbl1136.53027
  9. Miernowski, A., Mozgawa, W., Lift of the Finsler foliations to its normal bundle, Differential Geom. Appl. 24 (2006), 209-214.[Crossref] Zbl1095.53021
  10. Mihai, I., Roşca, R. and Verstraelen, L., Some aspects of the differential geometry of vector fields, PADGE, Katholieke Univ. Leuven, vol. 2 (1996). Zbl0960.53019
  11. Miron, R., Anastasiei, M., The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Acad. Publ., Dordrecht, 1994. Zbl0831.53001
  12. Popescu, P., Popescu, M., Lagrangians adapted to submersions and foliations, Differential Geom. Appl. 27 (2009), 171-178.[WoS][Crossref] Zbl1162.53019
  13. Singh, K. D., Singh, R., Some f(3, ε)-structure manifold, Demonstratio Math. 10 (3-4) (1977), 637-645. 
  14. Vaisman, I., Lagrange geometry on tangent manifolds, Int. J. Math. Math. Sci. 51 (2003), 3241-3266.[Crossref] Zbl1045.53021
  15. Yano, K., On a structure defined by a tensor field of type (1, 1) satisfying f3 + f = 0, Tensor (N.S.) 14 (1963), 99-109. Zbl0122.40705

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