Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 50 Sayı: 6, 1745 - 1755, 14.12.2021
https://doi.org/10.15672/hujms.678660

Öz

Kaynakça

  • [1] N. Aktan, M. Yıldırım and C. Murathan, Almost $f$-cosymplectic manifolds, Mediterr. J. Math., 11 (2), 775-787, 2014.
  • [2] M.A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat., 46 (2), 176-192, 2017.
  • [3] K.K. Baishya and P.R. Chowdhury, On Generalized weakly symmetric Kenmotsu man- ifolds, Bol. Soc. Paran. Mat., 39 (6), 211-222, 2021.
  • [4] S. Beyendi, G. Ayar and N. Aktan, On a type of $\alpha$-cosymplectic manifolds, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (1), 852-861, 2019.
  • [5] D.E. Blair, Contact Manifolds in Riemannian Geometry, Lect. Notes Math. 509, Springer-Verlag, Berlin, 1976.
  • [6] E. Cartan, Sur une classes remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54, 214-264, 1926.
  • [7] M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg. J. Physics, 15 (6), 526-531, 1988.
  • [8] U.C. De and S. Bandyopadhyay, On weakly symmetric spaces, Acta Math. Hung., 87(3), 205-212, 2000.
  • [9] R.S.D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math., 10 (12), 1508-1513, 1979.
  • [10] Y. Gündüzalp and M.A. Akyol, Conformal slant submersions from cosymplectic man- ifolds, Turk. J. Math., 42 (5), 2672-2689, 2018.
  • [11] S.K. Hui, A.A. Shaikh and I. Roy, On totaly umbilical hypersurfaces of weakly con- harmonically symmetric spaces, Global journal of Pure and Applied Mathematics, 10 (4), 28-31, 2010.
  • [12] S.K. Jana and A.A. Shaikh, On quasi-conformally flat weakly Ricci symmetric man- ifolds, Acta Math. Hung., 115 (3), 197-214, 2007.
  • [13] T.W. Kim and H.K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math, Sinica, Eng. Ser. Aug., 21 (4), 841-846, 2005.
  • [14] F. Özen and S. Altay, On weakly and pseudo symmetric Riemannian spaces, Indian J. Pure Appl. Math., 33 (10), 1477-1488, 2001.
  • [15] H. Öztürk, C. Murathan, N. Aktan and A.T. Vanli, Almost $\alpha$-cosymplectic $f$- manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 60 (1), 211-226, 2014.
  • [16] M. Prvanovic, On weakly symmetric Riemannian manifolds, Pub. Math. Debrecen, 46, 19-25, 1995.
  • [17] A.A. Shaikh and K.K.Baishya, On weakly quasi-conformally symmetric manifolds, Soochow Journal of Mathematics 31 (4), 581-595, 2005.
  • [18] L. Tamassy and T.Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Coll. Math. Soc., J. Bolyai, 56, 663-670, 1989.
  • [19] M. Tarafdar and M.A.A. Jawarneh, Semi-Pseudo Ricci Symmetric manifold, J. Indian Inst. Sci., 73, 591-596, 1993.
  • [20] A.G. Walker, On Ruses space of recurrent curvature, Proc. London Math. Soc., 52, 36-54, 1950.
  • [21] M. Yıldırım and S. Beyendi, On almost generalized weakly symmetric $\alpha$-cosymplectic manifolds, Univers. J. Math. Appl., 3 (4), 156-159, 2020.

On generalized weakly symmetric $\alpha$-cosymplectic manifolds

Yıl 2021, Cilt: 50 Sayı: 6, 1745 - 1755, 14.12.2021
https://doi.org/10.15672/hujms.678660

Öz

This study is concerned with some results on generalized weakly symmetric and generalized weakly Ricci-symmetric $\alpha$-cosymplectic manifolds. We prove the necessary and sufficient conditions for an $\alpha$-cosymplectic manifold to be generalized weakly symmetric and generalized weakly Ricci-symmetric. On the basis of these results, we give one proper example of generalized weakly symmetric $\alpha$-cosymplectic manifolds.

Kaynakça

  • [1] N. Aktan, M. Yıldırım and C. Murathan, Almost $f$-cosymplectic manifolds, Mediterr. J. Math., 11 (2), 775-787, 2014.
  • [2] M.A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat., 46 (2), 176-192, 2017.
  • [3] K.K. Baishya and P.R. Chowdhury, On Generalized weakly symmetric Kenmotsu man- ifolds, Bol. Soc. Paran. Mat., 39 (6), 211-222, 2021.
  • [4] S. Beyendi, G. Ayar and N. Aktan, On a type of $\alpha$-cosymplectic manifolds, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (1), 852-861, 2019.
  • [5] D.E. Blair, Contact Manifolds in Riemannian Geometry, Lect. Notes Math. 509, Springer-Verlag, Berlin, 1976.
  • [6] E. Cartan, Sur une classes remarquable d’espaces de Riemannian, Bull. Soc. Math. France, 54, 214-264, 1926.
  • [7] M.C. Chaki, On pseudo Ricci symmetric manifolds, Bulg. J. Physics, 15 (6), 526-531, 1988.
  • [8] U.C. De and S. Bandyopadhyay, On weakly symmetric spaces, Acta Math. Hung., 87(3), 205-212, 2000.
  • [9] R.S.D. Dubey, Generalized recurrent spaces, Indian J. Pure Appl. Math., 10 (12), 1508-1513, 1979.
  • [10] Y. Gündüzalp and M.A. Akyol, Conformal slant submersions from cosymplectic man- ifolds, Turk. J. Math., 42 (5), 2672-2689, 2018.
  • [11] S.K. Hui, A.A. Shaikh and I. Roy, On totaly umbilical hypersurfaces of weakly con- harmonically symmetric spaces, Global journal of Pure and Applied Mathematics, 10 (4), 28-31, 2010.
  • [12] S.K. Jana and A.A. Shaikh, On quasi-conformally flat weakly Ricci symmetric man- ifolds, Acta Math. Hung., 115 (3), 197-214, 2007.
  • [13] T.W. Kim and H.K. Pak, Canonical foliations of certain classes of almost contact metric structures, Acta Math, Sinica, Eng. Ser. Aug., 21 (4), 841-846, 2005.
  • [14] F. Özen and S. Altay, On weakly and pseudo symmetric Riemannian spaces, Indian J. Pure Appl. Math., 33 (10), 1477-1488, 2001.
  • [15] H. Öztürk, C. Murathan, N. Aktan and A.T. Vanli, Almost $\alpha$-cosymplectic $f$- manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (NS), 60 (1), 211-226, 2014.
  • [16] M. Prvanovic, On weakly symmetric Riemannian manifolds, Pub. Math. Debrecen, 46, 19-25, 1995.
  • [17] A.A. Shaikh and K.K.Baishya, On weakly quasi-conformally symmetric manifolds, Soochow Journal of Mathematics 31 (4), 581-595, 2005.
  • [18] L. Tamassy and T.Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Coll. Math. Soc., J. Bolyai, 56, 663-670, 1989.
  • [19] M. Tarafdar and M.A.A. Jawarneh, Semi-Pseudo Ricci Symmetric manifold, J. Indian Inst. Sci., 73, 591-596, 1993.
  • [20] A.G. Walker, On Ruses space of recurrent curvature, Proc. London Math. Soc., 52, 36-54, 1950.
  • [21] M. Yıldırım and S. Beyendi, On almost generalized weakly symmetric $\alpha$-cosymplectic manifolds, Univers. J. Math. Appl., 3 (4), 156-159, 2020.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Selahattin Beyendi 0000-0002-1037-6410

Mustafa Yıldırım 0000-0002-7885-1492

Yayımlanma Tarihi 14 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 6

Kaynak Göster

APA Beyendi, S., & Yıldırım, M. (2021). On generalized weakly symmetric $\alpha$-cosymplectic manifolds. Hacettepe Journal of Mathematics and Statistics, 50(6), 1745-1755. https://doi.org/10.15672/hujms.678660
AMA Beyendi S, Yıldırım M. On generalized weakly symmetric $\alpha$-cosymplectic manifolds. Hacettepe Journal of Mathematics and Statistics. Aralık 2021;50(6):1745-1755. doi:10.15672/hujms.678660
Chicago Beyendi, Selahattin, ve Mustafa Yıldırım. “On Generalized Weakly Symmetric $\alpha$-Cosymplectic Manifolds”. Hacettepe Journal of Mathematics and Statistics 50, sy. 6 (Aralık 2021): 1745-55. https://doi.org/10.15672/hujms.678660.
EndNote Beyendi S, Yıldırım M (01 Aralık 2021) On generalized weakly symmetric $\alpha$-cosymplectic manifolds. Hacettepe Journal of Mathematics and Statistics 50 6 1745–1755.
IEEE S. Beyendi ve M. Yıldırım, “On generalized weakly symmetric $\alpha$-cosymplectic manifolds”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 6, ss. 1745–1755, 2021, doi: 10.15672/hujms.678660.
ISNAD Beyendi, Selahattin - Yıldırım, Mustafa. “On Generalized Weakly Symmetric $\alpha$-Cosymplectic Manifolds”. Hacettepe Journal of Mathematics and Statistics 50/6 (Aralık 2021), 1745-1755. https://doi.org/10.15672/hujms.678660.
JAMA Beyendi S, Yıldırım M. On generalized weakly symmetric $\alpha$-cosymplectic manifolds. Hacettepe Journal of Mathematics and Statistics. 2021;50:1745–1755.
MLA Beyendi, Selahattin ve Mustafa Yıldırım. “On Generalized Weakly Symmetric $\alpha$-Cosymplectic Manifolds”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 6, 2021, ss. 1745-5, doi:10.15672/hujms.678660.
Vancouver Beyendi S, Yıldırım M. On generalized weakly symmetric $\alpha$-cosymplectic manifolds. Hacettepe Journal of Mathematics and Statistics. 2021;50(6):1745-5.