Some framed \(f\)-structures on transversally Finsler foliations

Cristian Ida

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 \(f(3,\varepsilon)\)-
structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.

Keywords


Transversally Finsler foliation; Liouville distribution; framed f-structures

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References


Abate, M., Patrizio, G., Finsler Metrics - A Global Approach, Lecture Notes in Math., 1591, Springer-Verlag, Berlin, 1994.

Anastasiei, M., A framed f-structure on tangent bundle of a Finsler space, An. Univ. Bucuresti, Mat.-Inf., 49 (2000), 3-9.

Bao, D., Chern, S. S. and Shen, Z., An Introduction to Riemannian Finsler Geometry, Graduate Texts in Math., 200, Springer-Verlag, New York, 2000.

Bejancu, A., Farran, H. R., On the vertical bundle of a pseudo-Finsler manifold, Int. J. Math. Math. Sci. 22 (3) (1997), 637-642.

Gırtu, M., An almost paracontact structure on the indicatrix bundle of a Finsler space, Balkan J. Geom. Appl. 7(2) (2002), 43-48.

Gırtu, M., A framed (f(3,-1))-structure on the tangent bundle of a Lagrange space, Demonstratio Math. 37(4) (2004), 955-961.

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.

Miernowski, A., A note on transversally Finsler foliations, Ann. Univ. Mariae Curie-Skłodowska Sect. A 60 (2006), 57-64.

Miernowski, A., Mozgawa, W., Lift of the Finsler foliations to its normal bundle, Differential Geom. Appl. 24 (2006), 209-214.

Mihai, I., Rosca, R. and Verstraelen, L., Some aspects of the differential geometry of vector fields, PADGE, Katholieke Univ. Leuven, vol. 2 (1996).

Miron, R., Anastasiei, M., The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Acad. Publ., Dordrecht, 1994.

Popescu, P., Popescu, M., Lagrangians adapted to submersions and foliations, Differential Geom. Appl. 27 (2009), 171-178.

Singh, K. D., Singh, R., Some (f(3,varepsilon))-structure manifold, Demonstratio Math. 10 (3-4) (1977), 637-645.

Vaisman, I., Lagrange geometry on tangent manifolds, Int. J. Math. Math. Sci. 51 (2003), 3241-3266.

Yano, K., On a structure defined by a tensor field of type (1, 1) satisfying (f^3 +f = 0), Tensor (N.S.) 14 (1963), 99-109.




DOI: http://dx.doi.org/10.17951/a.2011.65.1.87-96
Data publikacji: 2016-07-25 18:17:32
Data złożenia artykułu: 2016-07-25 17:56:01

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