The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The properties of these special Finsler spaces are studied and the relations between them are singled out.
1. H. Akbar-Zadeh, Initiation to global Finsler geometry, Elsevier, 2006.
2. J. Grifone, Structure pr´esque-tangente et connexions, I, Ann. Inst. Fourier, Grenoble, 22, 1 (1972), 287-334.
3. U. C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor, N. S., 56 (1995), 312-317.
4. Y. B. Maralabhavi and M. Rathnamma, On generalized recurrent manifold, Indian J. Pure Appl. Math., 30 (1999), 1167-1171.
5. M. Matsumoto, On h-isotropic and Ch-recurrent Finsler spaces, J. Math. Kyoto Univ., 11 (1971), 1-9.
6. R. S. Mishra and H. D. Pande, Recurrent Finsler spaces, J. Ind. Math. Soc., 32 (1968), 17-22.
7. R. H. Ojha, m-projectvely flat Saskian manifold, Indian J. Pure Appl. Math., 4 (1985), 481- 484.
8. E. M. Patterson, Some theorems on Ricci recurrent spaces, J. London Math. Soc., 27 (1952), 287-295.
9. S. K. Saha, On Type of Riemannian manifold, Bull. Cal. Math. Soc., 101 (2009), 553-558.
10. J. P. Singh, On an Einstein m-projectve P-Sasakian amnifolds, Bull. Cal. Math. Soc., 101 (2009), 175-180.
11. H. Singh and Q. Khan, On generalized recurrent Riemannian manifolds, Publ. Math. Debrecen, 56 (2000), 87-95.
12. A. G. Walker, On Ruses’s spaces of recurrent curvature, Proc. London Math. Soc., 52 (1950), 36-64.
13. Nabil L. Youssef and A. Soleiman, On concircularly recurrent Finsler manifolds, Balkan J. Geom. Appl., 18 (2013), 101-113.
14. Nabil L. Youssef and A. Soleiman, Some types of recurrence in Finsler geometry, submitted. arXiv: 1607.07468v2 [math.DG].
15. Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of special Finsler manifolds, J. Math. Kyoto Univ., 48 (2008), 857-893.
16. Nabil L. Youssef, S. H. Abed and A. Soleiman, A global theory of conformal Finsler geometry, Tensor, N. S., 69 (2008), 155–178.
17. Nabil L. Youssef, S. H. Abed and A. Soleiman, Cartan and Berwald connections in the pullback formalism, Algebras, Groups and Geometries, 25 (2008), 363–386.
18. Nabil L. Youssef, S. H. Abed and A. Soleiman, A global approach to the theory of connections in Finsler geometry, Tensor, N. S., 71 (2009), 187-208.
19. Nabil L. Youssef, S. H. Abed and A. Soleiman, Concurrent π-vector fields and eneregy β-change, Int. J. Geom. Meth. Mod. Phys., 6 (2009), 1003-1031.
20. Nabil L. Youssef, S. H. Abed and A. Soleiman, Geometric objects associated with the fundumental connections in Finsler geometry, J. Egypt. Math. Soc., 18 (2010), 67-90.
Soleiman, A. and Youssef, N. L. (2023). New special Finsler spaces. Journal of Finsler Geometry and its Applications, 4(1), 114-123. doi: 10.22098/jfga.2023.13112.1092
MLA
Soleiman, A. , and Youssef, N. L.. "New special Finsler spaces", Journal of Finsler Geometry and its Applications, 4, 1, 2023, 114-123. doi: 10.22098/jfga.2023.13112.1092
HARVARD
Soleiman, A., Youssef, N. L. (2023). 'New special Finsler spaces', Journal of Finsler Geometry and its Applications, 4(1), pp. 114-123. doi: 10.22098/jfga.2023.13112.1092
CHICAGO
A. Soleiman and N. L. Youssef, "New special Finsler spaces," Journal of Finsler Geometry and its Applications, 4 1 (2023): 114-123, doi: 10.22098/jfga.2023.13112.1092
VANCOUVER
Soleiman, A., Youssef, N. L. New special Finsler spaces. Journal of Finsler Geometry and its Applications, 2023; 4(1): 114-123. doi: 10.22098/jfga.2023.13112.1092
)