FINSLER SPACES WITH INFINITE SERIES (α, β)-METRIC

Title & Authors
FINSLER SPACES WITH INFINITE SERIES (α, β)-METRIC
Lee, Il-Yong; Park, Hong-Suh;

Abstract
In the present paper, we treat an infinite series ($\small{\alpha}$, $\small{\beta}$)-metric L =$\small{\beta}$$\small{^2}$/($\small{\beta}$-$\small{\alpha}$). First, we find the conditions that a Finsler metric F$\small{^{n}}$ with the metric above be a Berwald space, a Douglas space, and a projectively flat Finsler space, respectively. Next, we investigate the condition that a two-dimensional Finsler space with the metric above be a Landsbeg space. Then the differential equations of the geodesics are also discussed.愠䥮景牭慴楯渠慮搠䍯浭畮楣慴楯湳⁓潣楥瑹 k楣猑h瑴瀺⼯歩捳⹯爮歲渀ᔀ鳪떭鷫겼뗭閙谂ÁԳK潲敡渠卯捩整礠景爠䉩潴散桮潬潧礠慮搠䉩潥湧楮敥物湧Ѐ歩扢ᘀ桴瑰㨯⽷睷⹫獢戮潲⹫爯椀᠀鳪떭듬뚕鳪뎵駭验Ȁ섃ⴀ周攠䭯牥慮⁉湳瑩瑵瑥⁯映䉵楬摩湧⁃潮獴牵捴楯渄k楢挔h瑴瀺⼯睷眮歩挮潲⹫爀刀ᔀ鳪떭ꃬꂄ듭閙谂ÁЙK潲敡⁇敮潭攠佲条湩穡瑩潮̀歧漕h瑴瀺⼯睷眮歯杯⹯爮歲嬀ሀ胭閜胫ꚬ駭验Ȁ섅ἀ周攠䭯牥慮⁇敯杲慰桩捡氠卯捩整礃k杳ᬀ桴瑰㨯⽷睷⹫来潧牡灨礮潲⹫爀ഀ顝ﾖ⨀죡ﶖ⨀⢜ﾖ⨀増ﾖ⨀þﺖ⨀죗ﺖ⨀颒ﾖ⨀ ﺖ⨀ﺖ⨀䡯ﾖ⨀㣣ﺖ⨀꣖ﶖ⨀꣱ﺖ⨀烻ﶖ⨀࡜ﾖ⨀ピﶖ⨀tﾖ⨀堀ᔀ鳪떭胫나뗭閙谂ÁКK潲敡渠䝥潴散桩捡氠卯捩整礄k杴猙h瑴瀺⼯睷眮歧獨潭攮潲⹫爯䨀ༀ鳪떭䡃䧭閙谂Á̔H䍉⁓潣楥瑹⁯映䭯牥愄k档椗h瑴瀺⼯睷眮档楫潲敡⹯牧欀᠀鳪떭胬ꂕ蓭颸駭验Ȁ섃⌀周攠䭯牥慮⁁捡摥浩挠卯捩整礠潦⁈潭攄k档渠h瑴瀺⼯獯捩整礮歩獴椮牥⹫爯繫档渀堀ሀ鳪떭볪놰駭验Ȁ섄Ḁ周攠䭯牥慮⁈潵獩湧⁁獳潣楡瑩潮̀歨攙h瑴瀺⼯睷眮歨潵獩
Keywords
Berwald space;Douglas space;differential equations of geodesics;Finsler space;$\small{({\alpa}, {\beta})}$-metric;Landsberg space;projectively flat.;
Language
English
Cited by
1.
ON DOUGLAS SPACE WITH AN APPROXIMATE INFINITE SERIES $({\alpha},\;{\beta})$-METRIC,;

충청수학회지, 2009. vol.22. 4, pp.699-716
1.
RETRACTED: On two subclasses of -metrics being projectively related, Journal of Geometry and Physics, 2012, 62, 2, 292
2.
Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric, International Journal of Pure Mathematical Sciences, 2017, 18, 1
References
1.
Rep. Fac. Sci. Kagoshima Univ.(Math. Phys. Chem.), 1990. vol.23. pp.1-12

2.
The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, 1993.

3.
Publ. Math. Debrecen, 1996. vol.48. pp.357-366

4.
Publ. Math. Debrecen, 1997. vol.51. pp.385-406

5.
Tensor, N.S., 1994. vol.55. pp.252-257

6.
J. Korean Math. Soc., 1973. vol.10. pp.17-26

7.
Tensor, N.S., 1996. vol.57. pp.145-153

8.
J. Hokkaido Univ. Eduction(Sect.Ⅱ A 46(1995)), 1995. pp.1-10

9.
Foundations of Finsler Geometry and Special Finsler Spaces, 1986.

10.
Rep. Math. Phys., 1989. vol.28. pp.249-261

11.
Tensor, N.S., 1991. vol.50. pp.18-21

12.
Rep. Math. Phys., 1991. vol.30. pp.15-20

13.
Tensor, N.S., 1991. vol.50. pp.202-207

14.
Rep. Math. Phys., 1992. vol.31. pp.43-83

15.
Math. Comput. Modelling, 1994. vol.20. pp.1-23

16.
Tensor, N.S., 1998. vol.60. pp.123-134

17.
Roumaine Math. Pures Appl., 1997. vol.42. pp.9-10;787-793

18.
Commun. Korean Math. Soc., 1999. vol.14. 2, pp.373-383

19.
J. Korean Math. Soc., 2000. vol.37. 1, pp.73-84

20.
Indian J. pure and appl. Math., 2003. vol.34. 1, pp.59-77

21.
Tensor. N.S., 1977. vol.31. pp.219-226

22.
Rep. Math. Phys., 1977. vol.11. pp.347-360