Research Article
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Year 2021, , 1189 - 1196, 30.10.2021
https://doi.org/10.16984/saufenbilder.960842

Abstract

References

  • [1] H. Weyl, “Raum-Zeit-Materie”, J. Springer, 1918.
  • [2] A. G. Walker, “On Ruse's spaces of recurrent curvature,” Proc. Lond. Math., vol. 52, pp. 34-36, 1951.
  • [3] U. C. De and N. Guha, “On generalized recurrent manifolds,” J. National Academy of Math. India, vol. 9, pp. 85-92, 1991.
  • [4] K. Arslan, U. C. De, C. Murathan and A. Yıldız, “On generalized recurrent Riemannian manifolds,” Acta Math. Hungar., vol. 123 (1-2), pp. 27-39, 2009.
  • [5] T. Miyazawa, “On Riemannian space admitting some recurrent tensor,” Tru. Math. J., vol.2, pp. 11-18, 1996.
  • [6] U. C. De and A. K. Gazi, “On generalized concircularly recurrent manifolds,” Studia Scient. Math. Hungar., vol. 46(2), pp. 287- 296, 2009.
  • [7] E. M. Patterson, “Some theorems on Riccirecurrent spaces,” J. Lond. Math. Soc., vol. 27, pp. 287–295, 1952.
  • [8] U. C. De, N. Guha and D. Kamilya, “On generalized Ricci recurrent manifolds,” Tensor (NS), vol. 56, pp. 312–317, 1995.
  • [9] A. A. Shaikh, I. Roy and H. Kundu, “On some generalized recurrent manifolds”, Bull. Iranian Math. Soc., vol. 43(5), pp. 1209-1225, (2017).
  • [10] S. A. Uysal and H. B. Yılmaz, "Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold," Advances in Mathematical Physics, vol. 2020, Article ID 6831650, 4 pages, 2020.
  • [11] J. Kim, “On Almost Quasi Ricci Symmetric Manifolds,” Commun. Korean Math. Soc. Vol. 35, No. 2, pp. 603-611, 2020.
  • [12] E. Canfes, “On Generalized Recurrent Weyl Spaces and Wong's Conjecture,” Differential Geometry and Dynamical Systems, vol. 8, pp. 34-42, 2006.
  • [13] G. Gürpınar Arsan, G. Çivi Yıldırım, “Generalized concircular recurrent Weyl spaces,” Proceedings of the 4th International Colloquium Mathematics in Engineering and Numerical Physics, pp. 6- 8, 2006.
  • [14] U. C. De and A. K. Gazi, “On nearly quasi Einstein manifolds,” Novi Sad. J. Math., vol. 38(2), pp. 115–121, 2008.
  • [15] V. Hlavaty, “Theorie d'immersion d'une 𝑊𝑚 dans 𝑊𝑚,” Ann. Soc. Polon. Math., vol. 21, pp. 196-206, 1949.
  • [16] A. Norden, “Affinely Connected Spaces,” Nauka, Moscow, 1976.
  • [17] G. Zlatanov, “Nets in the n-dimensional Space of Weyl,” C. R. Aoad. Bulgare Sci., vol. 41, no. 10, pp 29-32, 1988.
  • [18] A. Özdeğer, “On sectional curvatures of Weyl manifolds,” Proc. Japan Acad, vol. 82A, no. 8, pp. 123-125, 2006.
  • [19] A. Özdeğer and Z. Şentürk, “Generalized Circles in Weyl spaces and their conformal mapping,” Publ. Math. Debrecen, vol. 60, no. 1-2, pp. 75-87, 2002.

On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds

Year 2021, , 1189 - 1196, 30.10.2021
https://doi.org/10.16984/saufenbilder.960842

Abstract

In the present work, generalized recurrent and generalized concircularly recurrent Weyl manifolds are examined. We define nearly quasi-Einstein Weyl manifolds and we proved that if a generalized recurrent or generalized concircularly recurrent Weyl manifold admits a special concircular vector field, then the manifold reduces to a nearly quasi-Einstein Weyl manifold. Also, some other results are presented.

References

  • [1] H. Weyl, “Raum-Zeit-Materie”, J. Springer, 1918.
  • [2] A. G. Walker, “On Ruse's spaces of recurrent curvature,” Proc. Lond. Math., vol. 52, pp. 34-36, 1951.
  • [3] U. C. De and N. Guha, “On generalized recurrent manifolds,” J. National Academy of Math. India, vol. 9, pp. 85-92, 1991.
  • [4] K. Arslan, U. C. De, C. Murathan and A. Yıldız, “On generalized recurrent Riemannian manifolds,” Acta Math. Hungar., vol. 123 (1-2), pp. 27-39, 2009.
  • [5] T. Miyazawa, “On Riemannian space admitting some recurrent tensor,” Tru. Math. J., vol.2, pp. 11-18, 1996.
  • [6] U. C. De and A. K. Gazi, “On generalized concircularly recurrent manifolds,” Studia Scient. Math. Hungar., vol. 46(2), pp. 287- 296, 2009.
  • [7] E. M. Patterson, “Some theorems on Riccirecurrent spaces,” J. Lond. Math. Soc., vol. 27, pp. 287–295, 1952.
  • [8] U. C. De, N. Guha and D. Kamilya, “On generalized Ricci recurrent manifolds,” Tensor (NS), vol. 56, pp. 312–317, 1995.
  • [9] A. A. Shaikh, I. Roy and H. Kundu, “On some generalized recurrent manifolds”, Bull. Iranian Math. Soc., vol. 43(5), pp. 1209-1225, (2017).
  • [10] S. A. Uysal and H. B. Yılmaz, "Some Properties of Generalized Einstein Tensor for a Pseudo-Ricci Symmetric Manifold," Advances in Mathematical Physics, vol. 2020, Article ID 6831650, 4 pages, 2020.
  • [11] J. Kim, “On Almost Quasi Ricci Symmetric Manifolds,” Commun. Korean Math. Soc. Vol. 35, No. 2, pp. 603-611, 2020.
  • [12] E. Canfes, “On Generalized Recurrent Weyl Spaces and Wong's Conjecture,” Differential Geometry and Dynamical Systems, vol. 8, pp. 34-42, 2006.
  • [13] G. Gürpınar Arsan, G. Çivi Yıldırım, “Generalized concircular recurrent Weyl spaces,” Proceedings of the 4th International Colloquium Mathematics in Engineering and Numerical Physics, pp. 6- 8, 2006.
  • [14] U. C. De and A. K. Gazi, “On nearly quasi Einstein manifolds,” Novi Sad. J. Math., vol. 38(2), pp. 115–121, 2008.
  • [15] V. Hlavaty, “Theorie d'immersion d'une 𝑊𝑚 dans 𝑊𝑚,” Ann. Soc. Polon. Math., vol. 21, pp. 196-206, 1949.
  • [16] A. Norden, “Affinely Connected Spaces,” Nauka, Moscow, 1976.
  • [17] G. Zlatanov, “Nets in the n-dimensional Space of Weyl,” C. R. Aoad. Bulgare Sci., vol. 41, no. 10, pp 29-32, 1988.
  • [18] A. Özdeğer, “On sectional curvatures of Weyl manifolds,” Proc. Japan Acad, vol. 82A, no. 8, pp. 123-125, 2006.
  • [19] A. Özdeğer and Z. Şentürk, “Generalized Circles in Weyl spaces and their conformal mapping,” Publ. Math. Debrecen, vol. 60, no. 1-2, pp. 75-87, 2002.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

İlhan Gül 0000-0002-0929-3503

Publication Date October 30, 2021
Submission Date July 1, 2021
Acceptance Date September 9, 2021
Published in Issue Year 2021

Cite

APA Gül, İ. (2021). On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds. Sakarya University Journal of Science, 25(5), 1189-1196. https://doi.org/10.16984/saufenbilder.960842
AMA Gül İ. On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds. SAUJS. October 2021;25(5):1189-1196. doi:10.16984/saufenbilder.960842
Chicago Gül, İlhan. “On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds”. Sakarya University Journal of Science 25, no. 5 (October 2021): 1189-96. https://doi.org/10.16984/saufenbilder.960842.
EndNote Gül İ (October 1, 2021) On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds. Sakarya University Journal of Science 25 5 1189–1196.
IEEE İ. Gül, “On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds”, SAUJS, vol. 25, no. 5, pp. 1189–1196, 2021, doi: 10.16984/saufenbilder.960842.
ISNAD Gül, İlhan. “On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds”. Sakarya University Journal of Science 25/5 (October 2021), 1189-1196. https://doi.org/10.16984/saufenbilder.960842.
JAMA Gül İ. On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds. SAUJS. 2021;25:1189–1196.
MLA Gül, İlhan. “On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds”. Sakarya University Journal of Science, vol. 25, no. 5, 2021, pp. 1189-96, doi:10.16984/saufenbilder.960842.
Vancouver Gül İ. On Generalized Recurrent and Generalized Concircularly Recurrent Weyl Manifolds. SAUJS. 2021;25(5):1189-96.

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