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On 4-th root metrics of isotropic scalar curvature

  • Akbar Tayebi
Veröffentlicht/Copyright: 13. Januar 2020
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 70 Heft 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.

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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
Schlagwörter für diesen Artikel
scalar curvature; 4-th root metric; weakly isotropic flag curvature

Artikel in diesem Heft

  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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