Vector Bundles and Paracontact Finsler Structures

Esmaeil Peyghan, Esa Sharahi

DOI Number
https://doi.org/10.22190/FUMI1802231P
First page
231
Last page
254

Abstract


Almost paracontact and normal almost paracontact Finsler structures on a vector bundle are defined. Finding some conditions, integrability of these structures are studied. Moreover, we define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find the vertical and horizontal flag curvatures. Then, defining vertical φ-flag curvature, we prove that every locally symmetric para-Sasakian Finsler structure has negative vertical φ-flag curvature. Finally, we define the horizontal and vertical Ricci tensors of a para-Sasakian Finsler structure and study some curvature properties of them.

Keywords

Finsler structure, paracontact structure, Sasakian structure, symmetry, vector bundle.

Keywords


Finsler structure, paracontact structure, Sasakian structure, symme- try, vector bundle

Full Text:

PDF

References


Bejan C. L and Drut¸ˇa-Romaniuc S. L., Connections which are harmonic with respect to general natural metrics, Diff. Geom. Appl. 30(2012), 306-317.

Calvaruso G., Symplectic, complex and K¨ahler structures on four-dimensional generalized symmetric spaces, Diff. Geom. Appl. 29(2011), 758-769.

Ivanov S, Vassilev D and Zamkovoy Z., Conformal paracontact curvature and the local flatness theorem, Geom. Dedicata, 144(2010), 79-100.

Kaneyuki S and Willams FL., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99(1985), 173-187.

Kazan A and Karada˘g HB., Paracontact Finsler Structures on Vector Bundles, British J. Math. Computer Sci., 4(24) (2014), 3403-3426.

Miron R, Hrimiuc D, Shimada H and Sabau SV., The Geometry of Hamilton and Lagrange Spaces, Kluwer. Acad. Pub. FTPH. 118, 2001.

Cappelletti-Montano B., Bi-Legendrian structures and paracontact geometry, Int. J. Geom. Methods Mod. Phys. 6(2009), 487-504.

Cappelletti-Montano B, Erken IK and Murathan C., Nullity conditions in paracontact geometry, Diff. Geom. Appl., 30(2012), 665-693.

Sasaki S., On paracontact Riemannian manifolds, TRU Math. 16(2) (1980), 75-86.

Sasaki S., On differentiable manifolds with certain structures which are closely related to almost contact structure, Tohoku. Math. J. 12(2)(1960), 459-476.

P Sato I., On a structure similar to the almost contact structure, Tensor (N. S), 30(1976), 219-224.

Sinha BB and Sai Prasad KL., Almost paracontact semi-symmetric metric Finsler connections on vector bundle, Indian J. Pure. Appl. Math, 26(3) (1995), 249-257.

Sinha BB and Yadav RK., An almost contact Finsler structures on vector bundle, Indian J. Pure. Appl. Math, 19(1) (1988), 27-35.

Sinha BB and Yadav RK., Almost contact semi-symmetric metric Finsler connections on vector bundle, Indian J. Pure. Appl. Math, 22(1) (1991), 29-39.

Vacaru SI and Vicol NA., Nonlinear connections and Clifford structures, arXiv: math/0205190v2 [math.DG], (2002).

Vacaru S., Superstrings in higher order extensions of Finsler superspaces, Nucl. Phys. B, 434(1997) 590-656.

Zamkovoy S., Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36(2009), 37-60.

Zamkovoy S., Canonical connections in paracontact manifolds, ArXiv: math/0707.1787v2 [math.DG], (2007).

Yalınıs AF and C¸alıs¸kan N., Sasakian Finsler manifolds, Turkish J. Math., 37 (2013), 319-339.




DOI: https://doi.org/10.22190/FUMI1802231P

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)