Istanbul Journal of Mathematics

SUBMITINFORMATION
EnglishTürkçe

Research Article


DOI :10.26650/ijmath.2023.00008   IUP :10.26650/ijmath.2023.00008    Full Text (PDF)

𝜁 (Ric)-vector fields on doubly warped product manifolds

Sibel Gerdan Aydın, Moctar Traore, Hakan Mete Taştan

We investigate 𝜁 (Ric)-vector fields on doubly warped product manifolds. We obtain some results when the vector field is also 𝜁 (Ric) on factor manifolds.We prove that if a vector field is a 𝜁 (Ric)-vector field on a doubly warped product manifold, it is also a 𝜁 (Ric)-vector field on the factor manifolds under certain conditions. Also, we show that a vector field on a doubly warped product manifold can be a 𝜁 (Ric)-vector field with some conditions. Moreover we give two important applications of this concept in the Lorentzian settings, which are the doubly warped product generalized Robertson-Walker space-time and doubly warped product standard static space-time.

Keywords: 𝜁(Ric)-vector field, warped product manifold, standard static space-times, generalized Robertson-Walker space-times

PDF View

References

  • Allison, D.E., 1988, Geodesic completeness in static space-times, Geom. Dedic., 26, 85-97. google scholar
  • Allison, D.E., 1998, Energy conditions in standard static space-times, Gen. Relativ. Gravit., 20(2), 115-122. google scholar
  • Allison, D.E., Ünal, B., 2003, Geodesic structure of standard static space-times, J. Geom. Phys. 46(2), 193–200. google scholar
  • Besse, A.L., 2007, Einstein Manifolds, Classics in Mathematics, Springer: Berlin, Germany. google scholar
  • Bishop, R. L., O’Neill, B., 1969, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145(1), 1-49. google scholar
  • Blaga, A.M., Taştan, H.M., 2022, Gradient solitons on doubly warped product manifolds, Rep. Math. Phys., 89(3), 319-333. google scholar
  • Chen, B.Y., 2017, Differential geometry of warped product manifolds and submanifolds, World Scientific. google scholar
  • Chen, B.Y., 2015, Some results on concircular vector fields and their applications to Ricci solitons, Bull. Korean Math. Soc., 52(5), 1535–1547. google scholar
  • De, U.C., Shenaway, S., Ünal, B., 2021, 𝜑(Ric)-vector fields on warped product manifolds and applications, Afr. Mat, 32, 1709-1716. google scholar
  • Ehrlich, P.E., 1974, Metric deformations of Ricci and sectional curvature on compact Riemannian manifolds, P.h.D. Dissertation, SUNNY Stony Brook, New York. google scholar
  • El-Sayied, H. K., Mantica, C. A., Shenawy, S. Syied, N., 2020, Gray’s Decomposition on Doubly Warped Product Manifolds and Applications, Filomat, 34(11), 3767-3776. google scholar
  • Flores, J.L., Sánchez, M., 2000, Geodesic connectedness and conjugate points in GRW spacetimes, J. Geom. Phys., 36(3-4), 285-314. google scholar
  • Gutierrez, M., Olea, B., 2012, Semi-Riemannian manifolds with a doubly warped structure, Rev. Mat. Iberoam., 28(1), 1-24. google scholar
  • Hinterleitner, I., Kiosak, V.A, 2008, 𝜑(Ric)-vector fields in Riemannian spaces, Arch. Math., 44(5), 385–390. google scholar
  • Hinterleitner, I., Kiosak, V.A, 2009, 𝜑(Ric)-vector fields on conformally flat spaces, AIP. Conf. Prof., 1191(1), 98-103. google scholar
  • Kırık, B., Özen Zengin, F., 2015, Conformal mappings of quasi-Einstein manifolds admitting special vector fields, Filomat, 29(3), 525–534. google scholar
  • Kırık, B., Özen Zengin, F., 2015, Generalized quasi-Einstein manifolds admitting special vector fields, Acta Math. Acad. Paedagog. Nyregyhziensis, 31(1), 61–69. google scholar
  • Kırık, B., Özen Zengin, F., 2019, Applications of a special generalized quasi-Einstein manifold, Bull.Iran.Math. Soc., 45, 89–102. google scholar
  • Kobayashi, S., 1995, Transformations groups in differential geometry, Classic in Mathematics, Springer: Berlin, Germany. google scholar
  • O’Neill, B., 1983, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Limited: London, England. google scholar
  • Sánchez, M., 1998, On the geometry of generalized Robertson–Walker spacetimes: geodesics, Gen. Relativ. Gravit., 30(6), 915-93. google scholar
  • Sánchez, M., 1999, On the geometry of generalized Robertson–Walker space times: curvature and killing fields, J. Geom. Phys., 31(1), 1-15. google scholar
  • Özen Zengin, F., Kırık, B., Conformal mappings of nearly quasi-Einstein manifolds, Miskolc Math. Notes, 14(2), 629–636. google scholar

Citations

Copy and paste a formatted citation or use one of the options to export in your chosen format


EXPORT



APA

Gerdan Aydın, S., Traore, M., & Taştan, H.M. (2023). 𝜁 (Ric)-vector fields on doubly warped product manifolds. Istanbul Journal of Mathematics, 1(2), 67-73. https://doi.org/10.26650/ijmath.2023.00008


AMA

Gerdan Aydın S, Traore M, Taştan H M. 𝜁 (Ric)-vector fields on doubly warped product manifolds. Istanbul Journal of Mathematics. 2023;1(2):67-73. https://doi.org/10.26650/ijmath.2023.00008


ABNT

Gerdan Aydın, S.; Traore, M.; Taştan, H.M. 𝜁 (Ric)-vector fields on doubly warped product manifolds. Istanbul Journal of Mathematics, [Publisher Location], v. 1, n. 2, p. 67-73, 2023.


Chicago: Author-Date Style

Gerdan Aydın, Sibel, and Moctar Traore and Hakan Mete Taştan. 2023. “𝜁 (Ric)-vector fields on doubly warped product manifolds.” Istanbul Journal of Mathematics 1, no. 2: 67-73. https://doi.org/10.26650/ijmath.2023.00008


Chicago: Humanities Style

Gerdan Aydın, Sibel, and Moctar Traore and Hakan Mete Taştan. “𝜁 (Ric)-vector fields on doubly warped product manifolds.” Istanbul Journal of Mathematics 1, no. 2 (May. 2024): 67-73. https://doi.org/10.26650/ijmath.2023.00008


Harvard: Australian Style

Gerdan Aydın, S & Traore, M & Taştan, HM 2023, '𝜁 (Ric)-vector fields on doubly warped product manifolds', Istanbul Journal of Mathematics, vol. 1, no. 2, pp. 67-73, viewed 18 May. 2024, https://doi.org/10.26650/ijmath.2023.00008


Harvard: Author-Date Style

Gerdan Aydın, S. and Traore, M. and Taştan, H.M. (2023) ‘𝜁 (Ric)-vector fields on doubly warped product manifolds’, Istanbul Journal of Mathematics, 1(2), pp. 67-73. https://doi.org/10.26650/ijmath.2023.00008 (18 May. 2024).


MLA

Gerdan Aydın, Sibel, and Moctar Traore and Hakan Mete Taştan. “𝜁 (Ric)-vector fields on doubly warped product manifolds.” Istanbul Journal of Mathematics, vol. 1, no. 2, 2023, pp. 67-73. [Database Container], https://doi.org/10.26650/ijmath.2023.00008


Vancouver

Gerdan Aydın S, Traore M, Taştan HM. 𝜁 (Ric)-vector fields on doubly warped product manifolds. Istanbul Journal of Mathematics [Internet]. 18 May. 2024 [cited 18 May. 2024];1(2):67-73. Available from: https://doi.org/10.26650/ijmath.2023.00008 doi: 10.26650/ijmath.2023.00008


ISNAD

Gerdan Aydın, Sibel - Traore, Moctar - Taştan, HakanMete. “𝜁 (Ric)-vector fields on doubly warped product manifolds”. Istanbul Journal of Mathematics 1/2 (May. 2024): 67-73. https://doi.org/10.26650/ijmath.2023.00008



TIMELINE


Submitted04.05.2023
Accepted24.10.2023
Published Online18.12.2023

LICENCE


Attribution-NonCommercial (CC BY-NC)

This license lets others remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms.


SHARE




Istanbul University Press aims to contribute to the dissemination of ever growing scientific knowledge through publication of high quality scientific journals and books in accordance with the international publishing standards and ethics. Istanbul University Press follows an open access, non-commercial, scholarly publishing.