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Dergiler / Istanbul Journal of Mathematics / 2023 / Volume: 1 Issue: 2

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

Sibel Gerdan Aydın(Istanbul University, Faculty of Science, Department of Mathematics)0000-0001-5278-6066
Moctar Traore(Istanbul University, Faculty of Science, Department of Mathematics)0000-0003-2132-789X
Hakan Mete Taştan(Istanbul University, Faculty of Science, Department of Mathematics)0000-0002-0773-9305
Sayfa
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Yayın Tarihi
2023-12-17
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We investigate 𝜁 (Ric)-vector fields on doubly warped product manifolds.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:𝜁(Ric)-vector field · warped product manifold · standard static space-times

Abstract

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.

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Bu Makaleye Atıf Yap

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

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Kaynakça (23)

  1. Allison, D.E., 1988, Geodesic completeness in static space-times, Geom. Dedic., 26, 85-97. google scholar
  2. Allison, D.E., 1998, Energy conditions in standard static space-times, Gen. Relativ. Gravit., 20(2), 115-122. google scholar
  3. Allison, D.E., Ünal, B., 2003, Geodesic structure of standard static space-times, J. Geom. Phys. 46(2), 193–200. google scholar
  4. Besse, A.L., 2007, Einstein Manifolds, Classics in Mathematics, Springer: Berlin, Germany. google scholar
  5. Bishop, R. L., O’Neill, B., 1969, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145(1), 1-49. google scholar
  6. Blaga, A.M., Taştan, H.M., 2022, Gradient solitons on doubly warped product manifolds, Rep. Math. Phys., 89(3), 319-333. google scholar
  7. Chen, B.Y., 2017, Differential geometry of warped product manifolds and submanifolds, World Scientific. google scholar
  8. 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
  9. 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
  10. 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
  11. 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
  12. Flores, J.L., Sánchez, M., 2000, Geodesic connectedness and conjugate points in GRW spacetimes, J. Geom. Phys., 36(3-4), 285-314. google scholar
  13. Gutierrez, M., Olea, B., 2012, Semi-Riemannian manifolds with a doubly warped structure, Rev. Mat. Iberoam., 28(1), 1-24. google scholar
  14. Hinterleitner, I., Kiosak, V.A, 2008, 𝜑(Ric)-vector fields in Riemannian spaces, Arch. Math., 44(5), 385–390. google scholar
  15. Hinterleitner, I., Kiosak, V.A, 2009, 𝜑(Ric)-vector fields on conformally flat spaces, AIP. Conf. Prof., 1191(1), 98-103. google scholar
  16. Kırık, B., Özen Zengin, F., 2015, Conformal mappings of quasi-Einstein manifolds admitting special vector fields, Filomat, 29(3), 525–534. google scholar
  17. 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
  18. Kırık, B., Özen Zengin, F., 2019, Applications of a special generalized quasi-Einstein manifold, Bull.Iran.Math. Soc., 45, 89–102. google scholar
  19. Kobayashi, S., 1995, Transformations groups in differential geometry, Classic in Mathematics, Springer: Berlin, Germany. google scholar
  20. O’Neill, B., 1983, Semi-Riemannian Geometry with Applications to Relativity, Academic Press Limited: London, England. google scholar
  21. Sánchez, M., 1998, On the geometry of generalized Robertson–Walker spacetimes: geodesics, Gen. Relativ. Gravit., 30(6), 915-93. google scholar
  22. 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
  23. Özen Zengin, F., Kırık, B., Conformal mappings of nearly quasi-Einstein manifolds, Miskolc Math. Notes, 14(2), 629–636. google scholar