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Projective Changes between Generalized (<i>α</i>, <i>β</i>)-Metric and Randers Metric
Department of Mathematics, School of Engineering, Presidency University, Bengaluru, India
Department of Mathematics, Sri Jagadguru Renukacharya College of Science, Arts and Commerce, Bengaluru, India
Department of Mathematics, Vemana Institute of Technology, Bengaluru, India
- 1 Department of Mathematics, School of Engineering, Presidency University, Bengaluru, India
- 2 Department of Mathematics, Sri Jagadguru Renukacharya College of Science, Arts and Commerce, Bengaluru, India
- 3 Department of Mathematics, Vemana Institute of Technology, Bengaluru, India
Advances in Pure Mathematics·Volume 10 (2020)·Pages 312–321·Published 30 April 2020·DOI10.4236/apm.2020.105018
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Abstract
Projective change between two Finsler metrics arises from Information Geom-etry. Such metrics have special geometric properties and will play an important role in Finsler geometry. The purpose of the present paper is to find a relation to characterize the projective change between generalized ( α , β ) - metric ( μ 1 , μ 2 and μ 3 ≠ 0 are constants) and Randers metric , where α and are two Riemannian metrics, β and are 1-forms. Further, we study such projective change when generalized ( α , β ) -metric F has some curvature property.
KeywordsFinsler Space with (<i>α</i><i>β</i>) -MetricProjective ChangeLocally Projectively FlatRanders Metric
- Cui, N. and Shen, Y.B. (2009) Projective Change between Two Classes of ( α , β ) -Metrics. Differential Geometry and Its Applications, 27, 566-573. https://doi.org/10.1016/j.difgeo.2009.03.003
- Jiang, J. and Cheng, X. (2012) Projective Changes between Two Important Classes of ( α , β ) -Metrics. Advances in Mathematics, 41, 732-740.
- Park, H. and Lee, Y. (1998) Projective Changes between a Finsler Space with ( α , β ) -Metric and Associated Riemannian Space. Tensor, 60, 327-331.
- Shen, Z. (2009) On Projectively Flat ( α , β ) -Metrics. Canadian Mathematical Bulletin, 52, 132-144. https://doi.org/10.4153/CMB-2009-016-2
- Narasimhamurthy, S.K. and Vasantha, D.M. (2012) Projective Change between Randers Metric and Special ( α , β ) -Metrics. Journal of Informatics and Mathematical Sciences, 4, 293-303.
- Kumar, P., Narasimhamurthy, S.K., Ramesha, M. and Madhu, T.S. (2019) On Projective Relation of Two Subclasses of ( α , β ) -Metrics. Global Journal of Engineering Science and Researches, 6, 223-231.
- Rapscak, A. (1961) Uber die bahntreuen Abbildungen metrisher Raume. Publicationes Mathematicae Debrecen, 8, 285-290.
- Bacso, S. and Matsumoto, M. (1994) Projective Change between Finsler Spaces with ( α , β ) -Metric. Tensor N. S., 55, 252-257.
- Kumar, P., Madhu, T.S. and Chandru, K. (2019) Einstein Finslerian Space with Special ( α , β ) -Metric. Journal of Computer and Mathematical Sciences, 10, 392-398. https://doi.org/10.29055/jcms/1019
- Basco, S. and Matsumoto, M. (1997) On Finsler Space of Douglas Type. A Generalization of the Notion of Berwald Space. Publicationes Mathematicae Debrecen, 51, 385-406.
- Tayebi, A. and Sadeghi, H. (2015) On Generalized Douglas-Weyl ( α , β ) -Metrics. Acta Mathematica Sinica, English Series, 31, 1611-1620. https://doi.org/10.1007/s10114-015-3418-2
- Benling, L. (2009) On a Class of Douglas Metrics in Finsler Geometry. Studia Scientiarum Mathematicarum Hungarica, 46, 355-365. https://doi.org/10.1556/SScMath.2009.1096
- Tayebi, A. and Barzegari, M. (2016) Generalized Berwald Spaces with ( α , β ) -Metrics. Indagationes Mathematicae, 27, 670-683.