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S-curvature for a new class of \((\alpha , \beta )\)-metrics

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Abstract

In this paper, we will investigate the S-curvature, the Landsberg curvature, mean Landsberg curvature, Cartan torsion and mean Cartan torsion for recently introduced \((\alpha , \beta )\)-metric \(F=\beta +\frac{a\alpha ^{2}+\beta ^{2}}{\alpha }\) in Pişcoran and Mishra (Georgian Math. J. (in press) 2016); where \(\alpha \) is a Riemannian metric; \(\beta \) is an 1-form and \(a\in (0,1]\) is a real positive scalar. We find the necessary and sufficient condition under which this class of Finsler metrics is Riemannian or locally Minkowskian. Finally, we prove that the above mentioned metric has bounded Cartan torsion.

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Authors and Affiliations

  1. North University Center of Baia Mare Technical University of Cluj Napoca Department of Mathematics and Computer Science, Victoriei 76, 430122, Baia Mare, Romania

    Laurian-Ioan Pişcoran

  2. Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev Dumas Road, Surat, Gujarat, 395 007, India

    Vishnu Narayan Mishra

Authors
  1. Laurian-Ioan Pişcoran
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  2. Vishnu Narayan Mishra
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Correspondence to Vishnu Narayan Mishra.

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Pişcoran, LI., Mishra, V.N. S-curvature for a new class of \((\alpha , \beta )\)-metrics. RACSAM 111, 1187–1200 (2017). https://doi.org/10.1007/s13398-016-0358-3

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  • DOI: https://doi.org/10.1007/s13398-016-0358-3

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