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Projective flatness of a new class of (α,β)-metrics

  • Laurian-Ioan Pişcoran and Vishnu Narayan Mishra ORCID logo EMAIL logo
Published/Copyright: August 12, 2017
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 26 Issue 1

Abstract

In this paper we investigate a new (α,β)-metric F=β+a⁢α2+β2α, where α=ai⁢j⁢yi⁢yj is a Riemannian metric; β=bi⁢yi is a 1-form and a∈(14,+∞) is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α.

Keywords: projectively flat
MSC 2010: 42C10; 46B07

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and valuable comments and suggestions that greatly contributed to improving the final version of the paper. They would also like to thank the editors for their generous comments and support during the reviewing process.

References

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Received: 2015-07-14
Revised: 2015-12-07
Accepted: 2015-12-10
Published Online: 2017-08-12
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/gmj-2017-0034
Keywords for this article
projectively flat

Articles in the same Issue

  1. Frontmatter
  2. Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound
  3. Isomorphism classes of weighted spaces of holomorphic functions on some subsets of complex plane
  4. Asymptotic behavior of solutions of fractional nabla q-difference equations
  5. A decomposition theorem for locally compact groups
  6. An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition
  7. Entire function sharing a small function with its mixed-operators
  8. Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems
  9. On the full transitivity of a cotorsion hull
  10. Comparison results for solutions of elliptic Neumann problems with lower-order terms via Steiner symmetrization
  11. On the formula of Cohen–Vogt relatively pointed topological semi-simplicial sets
  12. On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces
  13. On the generalized absolute convergence of Fourier series
  14. Embedding theorems for Besov–Morrey spaces of many groups of variables
  15. Projective flatness of a new class of (α,β)-metrics
  16. Spread relation of E-valued meromorphic functions and its application
  17. q-dual mixed volumes and Lp-intersection bodies
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