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Geodesics of a Special Multiply Warped Product Manifolds

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Abstract

Special multiply warped product manifold as the generalization of a singly warped product manifold which plays an important role in the geometry and physics were considered. Essentially geodesics of this multiply warped product manifold have been presented.

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References

  1. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, vol. 60. Springer, New York (1989)

    Book  Google Scholar 

  2. Beem, J.K., Ehrlich, P.E., Powell, T.H.G.: Warped product manifolds in relativity. In: Rassias, T.H.M., Rassias, G.M. (eds.) Selected Studies: Physics-Astrophysics, Mathematics, History of Science, North-Holland, Amsterdam, pp 41–56 (1982)

  3. Ben Youssif, N.M.: Geodesics on central symmetric warped product manifold. Acta. Math. Acad. Paedagog. Nyházi. 20, 79–81 (2004)

    MathSciNet  MATH  Google Scholar 

  4. Bishop, R.L., O’Neill, B.: Manifolds of negative curvature. Trans. Amer. Math. Soc. 145, 1–49 (1969)

    Article  MathSciNet  Google Scholar 

  5. Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics, vol. 203. Birkhäser, Boston (2002)

    Book  Google Scholar 

  6. Chen, B.Y.: Differential Geometry of Warped Product Manifolds and Submanifolds. World Scientific, New Jersey (2017)

    Book  Google Scholar 

  7. Chen, B.-Y., Wei, Sh.W.: Sharp growth estimates for warping functions in multiply warped product manifolds. J. Geom. Symmetry Phys. 52, 27–46 (2019)

    Article  MathSciNet  Google Scholar 

  8. Dobarro, F., Ünal, B.: Curvature of multiply warped products. J. Geom. Phys. 55, 75–106 (2005)

    Article  MathSciNet  Google Scholar 

  9. Faghfouri, M., Haji-Badali, A., Gholami, F.: On cosmological constant of generalized Robertson–Walker space-times. J. Math. Phys. 58, 053508 (2017)

    Article  MathSciNet  Google Scholar 

  10. Gholami, F., Darabi, F., Haji-Badali, A.: Multiply-warped product metrics and reduction of Einstein equations. Int. J. Geom. Methods Mod. Phys. 14, 1750021 (2017)

    Article  MathSciNet  Google Scholar 

  11. Lemes de Sousa, M., Pina, R.: Gradient Ricci solitons with structure of warped product. Results Math. 71, 825–840 (2017)

    Article  MathSciNet  Google Scholar 

  12. Ünal, B.: Multiply warped products. J. Geom. Phys. 34, 287–301 (2000)

    Article  MathSciNet  Google Scholar 

  13. O’Neill, B.: Semi-Riemannian Geometry: with Applications to Relativity. Academic Press, Londong (1983)

    MATH  Google Scholar 

  14. Nagy, P.T.: On bundle-like conform deformation of Riemannian submersion. Acta. Math. Acad. Sci. Hung. 39, 155–161 (1982)

    Article  Google Scholar 

  15. Nagy, P.T.: Non-horizontal geodesics of a Riemannian submersion. Acta. Sci. Math. Szeged 45, 347–355 (1983)

    MathSciNet  MATH  Google Scholar 

  16. Nölker, S.: Isometric immersions of warped products. Differ. Geom. Appl. 6, 1–30 (1996)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Basic Sciences Faculty, University of Bonab, Bonab, 5551761167, Iran

    Abbas Rezaei & Ali Haji-Badali

  2. Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

    Fereshteh Malek

Authors
  1. Abbas Rezaei
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  2. Fereshteh Malek
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  3. Ali Haji-Badali
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Correspondence to Ali Haji-Badali.

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Rezaei, A., Malek, F. & Haji-Badali, A. Geodesics of a Special Multiply Warped Product Manifolds. Vietnam J. Math. 49, 1275–1282 (2021). https://doi.org/10.1007/s10013-020-00454-8

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  • DOI: https://doi.org/10.1007/s10013-020-00454-8

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