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On 4-th root metrics of isotropic scalar curvature

  • Akbar Tayebi
Published/Copyright: January 13, 2020
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 70 Issue 1

Abstract

In this paper, we prove that every non-Riemannian 4-th root metric of isotropic scalar curvature has vanishing scalar curvature. Then, we show that every 4-th root metric of weakly isotropic flag curvature has vanishing scalar curvature. Finally, we find the necessary and sufficient condition under which the conformal change of a 4-th root metric is of isotropic scalar curvature.

Keywords: scalar curvature; 4-th root metric; weakly isotropic flag curvature
MSC 2010: Primary 53B40; Secondary 53C60

  1. Communicated by Július Korbaš

Acknowledgement

The author would like to thank Professors Behzad Najafi and Hideo Shimada for their valuable comments and their encouragements during preparation of this manuscript. Also, the author would like to thank the referee for his/her careful reading of the manuscript and exact suggestions.

References

[1] Akbar-Zadeh, H.: Initiation to Global Finslerian Geometry, Elsevier, 2006.Search in Google Scholar

[2] Akbar-Zadeh, H.: Sur les espaces de Finsler á courbures sectionnelles constantes, Bull. Acad. Roy. Belg. Cl. Sci. 74(5) (1988), 271–322.10.3406/barb.1988.57782Search in Google Scholar

[3] Akbar-Zadeh, H.: Generalized Einstein manifolds, J. Geom. Phys. 17 (1995), 342–380.10.1016/0393-0440(94)00052-2Search in Google Scholar

[4] Antonelli, P. L.—Ingarden, R.—Matsumoto, M.: The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Acad. Publ., Netherlands, 199).Search in Google Scholar

[5] Bao, D.—Chern, S. S.—Shen, Z.: An Introduction to Riemann-Finsler Geometry, Springer-Verlag, 2000.10.1007/978-1-4612-1268-3Search in Google Scholar

[6] Bácsó, S.—Cheng, X.: Finsler conformal transformations and the curvature invariance, Publ. Math. Debrecen 70(1-2) (2007), 221–231.10.5486/PMD.2007.3606Search in Google Scholar

[7] Bao, D.—Robles, C.: Ricci and flag curvatures in Finsler geometry, A Sampler of Riemann-Finsler Geometry, MSRI Publications 50 (2004), 198–256.Search in Google Scholar

[8] Cheng, X.—Yuan, M.: On Randers metrics of isotropic scalar curvature, Publ. Math. Debrecen 84 (2014), 63–74.10.5486/PMD.2014.5833Search in Google Scholar

[9] Li, B.—Shen, Z.: Ricci curvature tensor and non-Riemannian quantities, Canad. Math. Bull. 58 (2015), 530–537.10.4153/CMB-2014-063-4Search in Google Scholar

[10] Li, B.—Shen, Z.: On projectively flat fourth root metrics, Canad. Math. Bull. 55 (2012), 138–145.10.4153/CMB-2011-056-5Search in Google Scholar

[11] Najafi, B.—Shen, Z.—Tayebi, A.: Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata 131 (2008), 87–97.10.1007/s10711-007-9218-9Search in Google Scholar

[12] Shimada, H.: On Finsler spaces with metricai1i2…imyi1yi2…yimm, Tensor (N.S.) 33 (1979), 365–372.Search in Google Scholar

[13] Shimada, H.: On the Ricci tensors of particular Finsler spaces, J. Korean Math. Soc. 14 (1977), 41–63.Search in Google Scholar

[14] Tayebi, A.: On generalized 4-th root metrics of isotropic scalar curvature, Math. Slovaca 68 (2018), 907–928.10.1515/ms-2017-0154Search in Google Scholar

[15] Tayebi, A.: On the theory of 4-th root Finsler metrics, Tbil. Math. J. 12(1) (2019), 83–92.10.32513/tbilisi/1553565628Search in Google Scholar

[16] Tayebi, A.—Najafi, B.: On a class of homogeneous Finsler metrics, J. Geom. Phys. 140 (2019), 265–270.10.1016/j.geomphys.2019.01.006Search in Google Scholar

[17] Tayebi, A.—Najafi, B.: On m-th root Finsler metrics, J. Geom. Phys. 61 (2011), 1479–1484.10.1016/j.geomphys.2011.03.012Search in Google Scholar

[18] Tayebi, A.—Najafi, B.: On m-th root metrics with special curvature properties, C. R. Acad. Sci. Paris, Ser. I. 349 (2011), 691–693.10.1016/j.crma.2011.06.004Search in Google Scholar

[19] Tayebi, A.—Razgordani, M.: Four families of projectively flat Finsler metrics with K = 1 and their non-Riemannian curvature properties, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM 112 (2018), 1463–1485.10.1007/s13398-017-0443-2Search in Google Scholar

[20] Tayebi, A.—Razgordani, M.: On conformally flat fourth root (α, β)-metrics, Differential Geom. Appl. 62 (2019), 253–266.10.1016/j.difgeo.2018.12.002Search in Google Scholar

[21] Tayebi, A.—Shahbazi Nia, M.: A new class of projectively flat Finsler metrics with constant flag curvature K = 1, Differential Geom. Appl. 41 (2015), 123–133.10.1016/j.difgeo.2015.05.003Search in Google Scholar

[22] Xu, B.—Li, B.: On a class of projectively flat Finsler metrics with flag curvature K = 1, Differential Geom. Appl. 31 (2013), 524–532.10.1016/j.difgeo.2013.05.001Search in Google Scholar

[23] Yajima, T.—Nagahama, H.: Finsler geometry for nonlinear path of fluids flow through inhomogeneous media, Nonlinear Anal. Real World Appl. 25 (2015), 1–8.10.1016/j.nonrwa.2015.02.009Search in Google Scholar

[24] Yu, Y.—You, Y.: On Einstein m-th root metrics, Differential Geom. Appl. 28 (2010), 290–294.10.1016/j.difgeo.2009.10.011Search in Google Scholar
Received: 2019-03-14
Accepted: 2019-06-17
Published Online: 2020-01-13
Published in Print: 2020-02-25

© 2020 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0341
Keywords for this article
scalar curvature; 4-th root metric; weakly isotropic flag curvature

Articles in the same Issue

  1. Regular papers
  2. Doc. RNDr. Roman Frič, DrSc. – 3/4 C?
  3. Sugihara algebras and Sugihara monoids: Multisorted dualities
  4. Two by two squares in set partitions
  5. Identifying quantum logics by numerical events
  6. Some remarks on divisible polyhedral MV-algebras
  7. Remarks on b-metrics, ultrametrics, and metric-preserving functions
  8. Estimates of essential norm of generalized weighted composition operators from Bloch type spaces to nth weighted type spaces
  9. Maximum term of transcendental entire function and spider’s web
  10. Entire solutions of certain type of non-linear differential equations
  11. On the oscillatory behavior of third order differential equations with a sublinear neutral term
  12. Eigenvalue problems for a class of nonlinear Hadamard fractional differential equations with p-Laplacian operator
  13. The amalgam space L(p,q)π(G) on IN-groups
  14. On the topology of partial metric spaces
  15. The trace of the commutator of the Cesàro operator and a compact operator
  16. Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold
  17. On 4-th root metrics of isotropic scalar curvature
  18. On ultrametric-preserving functions
  19. Porosity of 𝓢-approximately continuous functions
  20. On a modified Burr XII distribution having flexible hazard rate shapes
  21. A study of chi-square-type distribution with geometrically distributed degrees of freedom in relation to distributions of geometric random sums
  22. An alternative estimate for the numerical radius of Hilbert space operators
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