ON COMPLEX FINSLER SPACES WITH RANDERS METRIC

Title & Authors
ON COMPLEX FINSLER SPACES WITH RANDERS METRIC
Aldea, Nicoleta; Munteanu, Gheorghe;

Abstract
In this paper we introduce in study a new class of complex Finsler spaces, namely the complex Randers spaces, for which the fundamental metric tensor and the Chern-Finsler connection are determined. A special approach is devoted to $\small{K{\ddot{a}}ahler}$-Randers metrics. Using the length arc parametrization for the extremal curves of the Euler-Lagrange equations we obtain a complex nonlinear connections of Lorentz type in a complex Randers space.
Keywords
complex Finsler spaces;Randers spaces;
Language
English
Cited by
1.
ON SOME CLASSES OF ℝ-COMPLEX HERMITIAN FINSLER SPACES,;;

대한수학회지, 2015. vol.52. 3, pp.587-601
1.
Projectively related complex Finsler metrics, Nonlinear Analysis: Real World Applications, 2012, 13, 5, 2178
2.
On complex Douglas spaces, Journal of Geometry and Physics, 2013, 66, 80
3.
On real and complex Berwald connections associated to strongly convex weakly Kähler–Finsler metric, Differential Geometry and its Applications, 2011, 29, 3, 388
4.
Recent results on complex Cartan spaces, Journal of Geometry and Physics, 2016, 106, 155
5.
A YANG–MILLS ELECTRODYNAMICS THEORY ON THE HOLOMORPHIC TANGENT BUNDLE, Journal of Nonlinear Mathematical Physics, 2010, 17, 2, 227
6.
Conformal Complex Landsberg Spaces, Annals of the Alexandru Ioan Cuza University - Mathematics, 2011, 57, Supliment
7.
On complex Landsberg and Berwald spaces, Journal of Geometry and Physics, 2012, 62, 2, 368
8.
About a special class of two-dimensional complex Finsler spaces, Indian Journal of Pure and Applied Mathematics, 2012, 43, 2, 107
9.
The main invariants of a complex finsler space, Acta Mathematica Scientia, 2014, 34, 4, 995
10.
Some results on strong Randers metrics, Periodica Mathematica Hungarica, 2015, 71, 1, 24
11.
ON COMPLEX RANDERS METRICS, International Journal of Mathematics, 2010, 21, 08, 971
12.
A COMPLEX FINSLER APPROACH OF GRAVITY, International Journal of Geometric Methods in Modern Physics, 2012, 09, 07, 1250058
13.
RETRACTED: Complex Bogoslovsky Finsler metrics, Journal of Mathematical Analysis and Applications, 2012, 391, 1, 159
14.
NEW CANDIDATES FOR A HERMITIAN APPROACH OF GRAVITY, International Journal of Geometric Methods in Modern Physics, 2013, 10, 09, 1350041
15.
On a Class of Smooth Complex Finsler Metrics, Results in Mathematics, 2017, 71, 3-4, 657
16.
Characterizations of complex Finsler connections and weakly complex Berwald metrics, Differential Geometry and its Applications, 2013, 31, 5, 648
References
1.
M. Abate and G. Patrizio, Finsler Metrics–A Global Approach. With Applications to Geometric Function Theory, Lecture Notes in Mathematics, 1591. Springer-Verlag, Berlin, 1994, x+180 pp

2.
T. Aikou, Projective Flatness of Complex Finsler Metrics, Publ. Math. Debrecen 63 (2003), no. 3, 343–362

3.
N. Aldea, Complex Finsler spaces of constant holomorphic curvature, Differential geometry and its applications, 179-190, Matfyzpress, Prague, 2005

4.
N. Aldea and G. Munteanu, ($\alpha$, $\beta$) -complex Finsler metrics, Proceedings of the 4th International Colloquium “Mathematics in Engineering and Numerical Physics”, 1-6, BGS Proc., 14, Geom. Balkan Press, Bucharest, 2007

5.
N. Aldea and G. Munteanu, On the geometry of complex Randers spaces, Proc. of the 14-th Nat. Sem. on Finsler, Lagrange and Hamilton spaces, Brasov, 2006, 1-8

6.
D. Bao, S. S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry, Graduate Texts in Mathematics 200, Springer-Verlag, New York, 2000, xx+431 pp

7.
D. Bao and C. Robles, On Randers spaces of constant flag curvature, Rep. Math. Phys. 51 (2003), no. 1, 9-42

8.
D. Bao, C. Robles, and Z. Shen, Zermelo navigation on Riemannian manifolds, J. Differential Geom. 66 (2004), no. 3, 377-435

9.
B. Chen and Y. Shen, Complex Randers Metrics, communicated to Conference Zhejiang Univ., China, July, 2007

10.
M. Fukui, Complex Finsler manifolds, J. Math. Kyoto Univ. 29 (1989), no. 4, 609–624

11.
R. S. Ingarden, On the geometrically absolute optical representation in the electron microscope, Trav. Soc. Sci. Lett. Wrochlaw, Ser. B. 1957 (1957), no. 3, 60 pp

12.
S. Kobayashi and C. Horst, Topics in complex differential geometry. Complex Differential Geometry, 4–66, DMV Sem. 3. Birkhauser, Basel, 1983

13.
M. Matsumoto, Randers spaces of constant curvature, Rep. Math. Phys. 28 (1989), no. 2, 249–261

14.
R. Miron, The geometry of Ingarden spaces, Rep. Math. Phys. 54 (2004), no. 2, 131–147

15.
G. Munteanu, Complex Spaces in Finsler, Lagrange and Hamilton Geometries, Fundamental Theories of Physics, 141. Kluwer Academic Publishers, Dordrecht, 2004, xii+221 pp.

16.
S. Nishikawa, Harmonic maps of Finsler manifolds, Topics in differential geometry, Ed. Academiei Romane, Bucuresti 2008, 208–247

17.
H. L. Royden, Complex Finsler metrics, Complex differential geometry and nonlinear differential equations (Brunswick, Maine, 1984), 119–124, Contemp. Math., 49, Amer. Math. Soc., Providence, RI, 1986

18.
A. Spiro, The Structure Equations of a Complex Finsler Manifold, Asian J. Math. 5 (2001), no. 2, 291–326

19.
P.-M. Wong, A survey of complex Finsler geometry. Finsler geometry, Sapporo 2005–in memory of Makoto Matsumoto, 375–433, Adv. Stud. Pure Math. 48, Math. Soc. Japan, Tokyo, 2007

20.
R. Yan, Connections on complex Finsler manifold, Acta Math. Appl. Sin., Engl. Ser. 19, (2003), no. 3, 431–436

21.
H. Yasuda and H. Shimada, On Randers spaces of scalar curvature, Rep. Mathematical Phys. 11 (1977), no. 3, 347–360