Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 6 Sayı: 1, 128 - 133, 15.04.2018

Öz

Kaynakça

  • [1] N. Aktan and A. Gorgulu, On weak symmetries of almost r􀀀para contact Riemannian manifold of P􀀀Sasakian type, Diff. Geom. Dyn. Syst. 9, (2007), 1-8.
  • [2] N. Aktan, S. Balkan and M. Yildirim, On weak symmetries of almost Kenmotsu (k, m, n)-spaces, Hacettepe J. Math. & Statistic 42 (4), (2013), 447-453.
  • [3] S. R. Ashoka, C. S. Bagewadi and G. Ingalahalli, Certain results on Ricci soliton in a􀀀Sasakian manifolds, Hindawi Publ. Corporation, Geometry Article ID573925, (2013), 4 pages.
  • [4] S. R. Ashoka, C. S. Bagewadi and G. Ingalahalli, Geometry on Ricci soliton in (LCS)n􀀀manifolds, Diff. Geom. Dyn. Syst. 16, (2014), 50-62.
  • [5] G. Ingalahalli and C. S. Bagewadi, Ricci soliton in Sasakian manifold, ISRN Geometry Article ID 521384, (2012), 13 pages.
  • [6] C. S. Bagewadi and G. Ingalalli, Ricci soliton on LP-Sasakian manifolds, Acta Math. Acad. Paedagog. Nyhazi. 28 (1), (2012), 59-68.
  • [7] C. L. Bejan and M. Crasmareanu, Ricci soliton on a manifold with quasi constant curvature, Publ. Math. Debrecen 78 (1), (2011), 235-243.
  • [8] B. Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl. 19 (1), (2014), 13-21.
  • [9] M. C. Chaki, On pseudo Ricci symmetric manifolds, Bulgar J. Phys. 15, (1988), 526-531.
  • [10] A. Carriazo and V. Martin-Molina, Almost cosymplectic and almost Kenmotsu (k, m, n)-paces, Mediterranean Journal of Mathematics 10 (3), (2013), 1551-1571.
  • [11] S. K. Chaubey and R. H. Ojha, On the m􀀀projective curvature tensor of a Kenmotsu manifold, Differential Geometry- Dynamical Systems 12, (2010), 52-60.
  • [12] S. K. Chaubey and C. S. Prasad, On generalized f􀀀recurrent Kenmotsu manifolds, TWMS J. App. Eng. Math. 5 (1), (2015), 1-9.
  • [13] S. K. Chaubey, S. Prakash and R. Nivas, Some properties of m􀀀projective curvature tensor in Kenmotsu manifolds, Bulletin of Math Analysis and Applications 4, (2012), 48-56.
  • [14] S. K. Chaubey, On weakly m􀀀projectively symmetric manifolds, Novi sad J. Math. 42 (1), (2012), 67-79.
  • [15] T. Chave and G. Valent, Quasi-Einstein metrics and their renoimalizability properties, Helv. Phys. Acta. 69, (1996), 344-347.
  • [16] S. K. Chaubey, Existence of N(k)􀀀quasi Einstein manifolds, Facta universititatis (NIS˘) Ser. Math. Inform. Vol. 32 (3), (2017), 369–385.
  • [17] Chow, B. and Knopf, D., The Ricci flow. An introduction-Mathematical Surveys and monographs 110, American Maths. Soc., 2004.
  • [18] T. Chave and G. Valent, On a class of compact and non-compact quasi-Einstein metrics and their renoimalizability properties, Nuclear Phys. B. 478, (1996), 758-778.
  • [19] U. C. De, T. Q. Binh and A. A. Shaikh, On weak symmetric and weakly Ricci symmetric K-contact manifolds, Acta Mathematica Acadeiae Paedagogicae Nayiregyhaziensis 16, (2000), 65-71.
  • [20] Derdzinski, A., Compact Ricci solitons, Preprint.
  • [21] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain geometric properties of h􀀀Ricci soliton on h􀀀Einstein Para-Kenmotsu manifolds, Palestine Journal of Mathematics vol.7, (2018), ??.
  • [22] D. H. Friedan, Non linear models in 2+e dimensions, Ann. Phys. 163, (1985), 318-419.
  • [23] R. S. Hamilton, The Ricci flow on the surfaces, Mathematics and general relativity, (Santa Cruz, CA, 1986), Contemp. Mathe. 71, American Math. Soc. (1988), 237-262.
  • [24] T. Ivey, Ricci soliton on compact 3-manifolds, Diff. Geo. Appl. 3, (1993), 301-307.
  • [25] T. Koufogiorgos, M. Markellos and V. J. Papantoiou, The harmonicity of the Reeb vector field on a contact metric 3􀀀manifolds, Pacific J. Math. 234 (2), (2008), 325-344.
  • [26] K. Kemotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24, (1972), 93-103.
  • [27] H. G. Nagaraja and C. R. Premlatta, Ricci soliton in Kenmotsu manifolds, J. Math. Anal. 3 (2), (2012), 18-24.
  • [28] H. Özturk and N. Aktan and C. Murathan, Alomst a􀀀cosymplectic spaces, arXiv: 1007.0527v1.
  • [29] C. Özgür, On weak symmetries of LP-Sasakian manifolds, Radovi Matamaticki 11, (2002), 263-270.
  • [30] S. K. Chaubey, Some properties of LP-Sasakian manifolds equipped with m􀀀projective curvature tensor, Bulletin of Mathematical Analysis and Applications 3 (4), (2011), 50-58.
  • [31] C. Özgür, On weakly symmetric Kenmotsu manifolds, Differential Geometry-Dynamical Systems 8, (2006), 204-209.
  • [32] L. Tamassy and T. Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor N. S. 53, (1993), 104-148.
  • [33] L. Tamassy and T. Q. Binh, On weak symmetric and weakly projective symmetric Riemannian manifolds, Coll. Math. Soc. J. Bolyai 56, (1992), 663-670.
  • [34] S. K. Yadav and P. K. Dwivedi, On Con harmonically and Special weakly Ricci symmetric Lorentzian Beta-Kenmotsu manifolds, International Journal of Mathematics science and Engineering -Application Vol.4 (5), (2010), 89-96.
  • [35] S. K. Yadav and D. L. Suthar, On Kenmotsu manifold satisfying certain condition, Journal of Tensor Society Vol. 3, (2009), 19-26.
  • [36] S. K. Yadav and Ajay Sriwastwa, A Note on x􀀀flat Kenmotsu manifolds, J. Nat. Acd. Math. Vol. 22, (2008), 77-82.

Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces

Yıl 2018, Cilt: 6 Sayı: 1, 128 - 133, 15.04.2018

Öz

The present paper deals with the study of Ricci soliton on weak symmetries of almost Kenmotsu $(\kappa ,\mu ,\nu)-$space and its geometric properties. Also, we obtain the condition for Ricci soliton on weakly symmetric and weakly Ricci symmetric almost Kenmotsu $(\kappa ,\mu ,\nu)-$space with the tensor field ${\rm \pounds }_{\xi }g +2S$ is parallel to be shrinking, steady and expanding respectively.

Kaynakça

  • [1] N. Aktan and A. Gorgulu, On weak symmetries of almost r􀀀para contact Riemannian manifold of P􀀀Sasakian type, Diff. Geom. Dyn. Syst. 9, (2007), 1-8.
  • [2] N. Aktan, S. Balkan and M. Yildirim, On weak symmetries of almost Kenmotsu (k, m, n)-spaces, Hacettepe J. Math. & Statistic 42 (4), (2013), 447-453.
  • [3] S. R. Ashoka, C. S. Bagewadi and G. Ingalahalli, Certain results on Ricci soliton in a􀀀Sasakian manifolds, Hindawi Publ. Corporation, Geometry Article ID573925, (2013), 4 pages.
  • [4] S. R. Ashoka, C. S. Bagewadi and G. Ingalahalli, Geometry on Ricci soliton in (LCS)n􀀀manifolds, Diff. Geom. Dyn. Syst. 16, (2014), 50-62.
  • [5] G. Ingalahalli and C. S. Bagewadi, Ricci soliton in Sasakian manifold, ISRN Geometry Article ID 521384, (2012), 13 pages.
  • [6] C. S. Bagewadi and G. Ingalalli, Ricci soliton on LP-Sasakian manifolds, Acta Math. Acad. Paedagog. Nyhazi. 28 (1), (2012), 59-68.
  • [7] C. L. Bejan and M. Crasmareanu, Ricci soliton on a manifold with quasi constant curvature, Publ. Math. Debrecen 78 (1), (2011), 235-243.
  • [8] B. Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl. 19 (1), (2014), 13-21.
  • [9] M. C. Chaki, On pseudo Ricci symmetric manifolds, Bulgar J. Phys. 15, (1988), 526-531.
  • [10] A. Carriazo and V. Martin-Molina, Almost cosymplectic and almost Kenmotsu (k, m, n)-paces, Mediterranean Journal of Mathematics 10 (3), (2013), 1551-1571.
  • [11] S. K. Chaubey and R. H. Ojha, On the m􀀀projective curvature tensor of a Kenmotsu manifold, Differential Geometry- Dynamical Systems 12, (2010), 52-60.
  • [12] S. K. Chaubey and C. S. Prasad, On generalized f􀀀recurrent Kenmotsu manifolds, TWMS J. App. Eng. Math. 5 (1), (2015), 1-9.
  • [13] S. K. Chaubey, S. Prakash and R. Nivas, Some properties of m􀀀projective curvature tensor in Kenmotsu manifolds, Bulletin of Math Analysis and Applications 4, (2012), 48-56.
  • [14] S. K. Chaubey, On weakly m􀀀projectively symmetric manifolds, Novi sad J. Math. 42 (1), (2012), 67-79.
  • [15] T. Chave and G. Valent, Quasi-Einstein metrics and their renoimalizability properties, Helv. Phys. Acta. 69, (1996), 344-347.
  • [16] S. K. Chaubey, Existence of N(k)􀀀quasi Einstein manifolds, Facta universititatis (NIS˘) Ser. Math. Inform. Vol. 32 (3), (2017), 369–385.
  • [17] Chow, B. and Knopf, D., The Ricci flow. An introduction-Mathematical Surveys and monographs 110, American Maths. Soc., 2004.
  • [18] T. Chave and G. Valent, On a class of compact and non-compact quasi-Einstein metrics and their renoimalizability properties, Nuclear Phys. B. 478, (1996), 758-778.
  • [19] U. C. De, T. Q. Binh and A. A. Shaikh, On weak symmetric and weakly Ricci symmetric K-contact manifolds, Acta Mathematica Acadeiae Paedagogicae Nayiregyhaziensis 16, (2000), 65-71.
  • [20] Derdzinski, A., Compact Ricci solitons, Preprint.
  • [21] S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain geometric properties of h􀀀Ricci soliton on h􀀀Einstein Para-Kenmotsu manifolds, Palestine Journal of Mathematics vol.7, (2018), ??.
  • [22] D. H. Friedan, Non linear models in 2+e dimensions, Ann. Phys. 163, (1985), 318-419.
  • [23] R. S. Hamilton, The Ricci flow on the surfaces, Mathematics and general relativity, (Santa Cruz, CA, 1986), Contemp. Mathe. 71, American Math. Soc. (1988), 237-262.
  • [24] T. Ivey, Ricci soliton on compact 3-manifolds, Diff. Geo. Appl. 3, (1993), 301-307.
  • [25] T. Koufogiorgos, M. Markellos and V. J. Papantoiou, The harmonicity of the Reeb vector field on a contact metric 3􀀀manifolds, Pacific J. Math. 234 (2), (2008), 325-344.
  • [26] K. Kemotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24, (1972), 93-103.
  • [27] H. G. Nagaraja and C. R. Premlatta, Ricci soliton in Kenmotsu manifolds, J. Math. Anal. 3 (2), (2012), 18-24.
  • [28] H. Özturk and N. Aktan and C. Murathan, Alomst a􀀀cosymplectic spaces, arXiv: 1007.0527v1.
  • [29] C. Özgür, On weak symmetries of LP-Sasakian manifolds, Radovi Matamaticki 11, (2002), 263-270.
  • [30] S. K. Chaubey, Some properties of LP-Sasakian manifolds equipped with m􀀀projective curvature tensor, Bulletin of Mathematical Analysis and Applications 3 (4), (2011), 50-58.
  • [31] C. Özgür, On weakly symmetric Kenmotsu manifolds, Differential Geometry-Dynamical Systems 8, (2006), 204-209.
  • [32] L. Tamassy and T. Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor N. S. 53, (1993), 104-148.
  • [33] L. Tamassy and T. Q. Binh, On weak symmetric and weakly projective symmetric Riemannian manifolds, Coll. Math. Soc. J. Bolyai 56, (1992), 663-670.
  • [34] S. K. Yadav and P. K. Dwivedi, On Con harmonically and Special weakly Ricci symmetric Lorentzian Beta-Kenmotsu manifolds, International Journal of Mathematics science and Engineering -Application Vol.4 (5), (2010), 89-96.
  • [35] S. K. Yadav and D. L. Suthar, On Kenmotsu manifold satisfying certain condition, Journal of Tensor Society Vol. 3, (2009), 19-26.
  • [36] S. K. Yadav and Ajay Sriwastwa, A Note on x􀀀flat Kenmotsu manifolds, J. Nat. Acd. Math. Vol. 22, (2008), 77-82.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

S. K. Chaubey

S. Yadav

Yayımlanma Tarihi 15 Nisan 2018
Gönderilme Tarihi 30 Haziran 2017
Kabul Tarihi 6 Nisan 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 1

Kaynak Göster

APA Chaubey, S. K., & Yadav, S. (2018). Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces. Konuralp Journal of Mathematics, 6(1), 128-133.
AMA Chaubey SK, Yadav S. Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces. Konuralp J. Math. Nisan 2018;6(1):128-133.
Chicago Chaubey, S. K., ve S. Yadav. “Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces”. Konuralp Journal of Mathematics 6, sy. 1 (Nisan 2018): 128-33.
EndNote Chaubey SK, Yadav S (01 Nisan 2018) Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces. Konuralp Journal of Mathematics 6 1 128–133.
IEEE S. K. Chaubey ve S. Yadav, “Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces”, Konuralp J. Math., c. 6, sy. 1, ss. 128–133, 2018.
ISNAD Chaubey, S. K. - Yadav, S. “Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces”. Konuralp Journal of Mathematics 6/1 (Nisan 2018), 128-133.
JAMA Chaubey SK, Yadav S. Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces. Konuralp J. Math. 2018;6:128–133.
MLA Chaubey, S. K. ve S. Yadav. “Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces”. Konuralp Journal of Mathematics, c. 6, sy. 1, 2018, ss. 128-33.
Vancouver Chaubey SK, Yadav S. Certain Results on Almost Kenmotsu $(\kappa ,\mu ,\nu)-$Spaces. Konuralp J. Math. 2018;6(1):128-33.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.