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A Note on Ricci Solitons on Para-Sasakian Manifolds

Yıl 2018, Cilt: 11 Sayı: 2, 237 - 242, 31.08.2018
https://doi.org/10.18185/erzifbed.402310

Öz

In the present paper, in an almost para-contact
metric manifold, especially on para-Sasakian manifolds,  Ricci solitons were examined. Also, we
consider the generalized quasi-conformal
curvature tensor
on a para-Sasakian manifold admitting Ricci soliton.

Kaynakça

  • Acet, B.E., Yüksel Perktaş, S., Kılıç, E. 2014. On lightlike geometry of para-Sasakian manifolds. Scientific Work Journal, Article ID 696231.
  • Acet, B.E. Yüksel Perktaş, S., Kılıç, E. 2016. On submanifolds of para-Sasakian manifolds. JP Journal of Geometry and Topology, 19, 1-18.
  • Adara, A.M, Yüksel Perktaş, S. Acet, B.E. Erdoğan, E.F. 2018. Ricci solitons in almost paracontact metric manifolds. Glasnik Matematicki, 53(73), 205-220.
  • Baishya, K.K., Chawdhury, P.B. 2016. On generalized quasi-conformal manifolds. Communication Korean Mathematics Society, 31, 163-176.
  • Calin, C., Crasmareanu, M. 2010. From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds. Bulletin of the Malaysian Mathematical Sciences Society, 33, 361-368.
  • Cortés, V. Lawn, M.A., Schäfer, L. 2006. Affine hyperspheres associated to special para-Kähler manifolds. International Journal of Geometric Methods in Modern Physic, 3, 995-1009.
  • De, U.C. Turan, M. Yıldız, A., De, A. 2012. Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds. Publicationes Mathematicae Debrecen, 80, 1-16.
  • Eisenhart, L.P. 1949. Riemannian geometry. J Princeton University Press.
  • Erdem, S. 2002. On almost (para) contact (hyperbolic) metric manifolds and harmonicity of holomorphic maps between them. Houston Journal of Mathematics, 28, 21-45.
  • Hamilton, R.S. 1982. Three-manifolds with positive Ricci curvature. Journal of Differential Geometry, 17, 301-308.
  • Hodesh, O., Fong, F.T.H. 2013. Rotational symmetry of canonical Kähler-Ricci solitons. arXiv: 1304.0277v2.
  • Ishii, Y. 1957. On conharmonic transformation. Tensor (N.S.), 7, 73-80.
  • Kaneyuki, S., Konzai, M. 1985. Paracomplex structure and affine symmetric spaces. Tokyo Journal of Mathematics, 8, 301-308.
  • Pokhariyal, G.P., Mishra, R.S. 1970. Curvature tensor and relativistics significance. Yokohama Mathematics Journal, 18, 105-108.
  • Turan, M. De, U.C., Yıldız, A. 2012. Ricci solitons and gradient Ricci solitons in 3-dimensional trans-Sasakian manifolds. Filomat, 26, 363-370.
  • Yano, K., Sawaki, S. 1968. Riemannian manifolds admitting a conformal transformation group. Journal of Differential Geometry, 2, 161-184.
  • Yano, K., Bochner, S. 1953. Curvature and Betti numbers. Annals of Mathematics Studies, 32, Princeton University Press.
  • Yüksel Perktaş, S. and Keleş, S. 2015. Ricci solitons in 3-dimensional normal almost paracontact metric manifolds. International Electronic Journal of Geometry, 8, 34-45.
  • Zamkovoy, S. 2009. Canonical connection on paracontact manifolds. Annals of Global Analysis and Geometry, 36, 37-60.

A Note on Ricci Solitons on Para-Sasakian Manifolds

Yıl 2018, Cilt: 11 Sayı: 2, 237 - 242, 31.08.2018
https://doi.org/10.18185/erzifbed.402310

Öz

Bu çalışmada, bir hemen hemen para-kontakt
metrik manifoldda, özellikle para-Sasakian manifoldlar üzerinde, Ricci
solitonlar incelenmiştir. Ayrıca bir para-Sasakian manifold üzerinde Ricci
soliton şartı ile birlikte genelleştirilmiş
quasi-conformal eğrilik tensörü
ele alınmıştır.

Kaynakça

  • Acet, B.E., Yüksel Perktaş, S., Kılıç, E. 2014. On lightlike geometry of para-Sasakian manifolds. Scientific Work Journal, Article ID 696231.
  • Acet, B.E. Yüksel Perktaş, S., Kılıç, E. 2016. On submanifolds of para-Sasakian manifolds. JP Journal of Geometry and Topology, 19, 1-18.
  • Adara, A.M, Yüksel Perktaş, S. Acet, B.E. Erdoğan, E.F. 2018. Ricci solitons in almost paracontact metric manifolds. Glasnik Matematicki, 53(73), 205-220.
  • Baishya, K.K., Chawdhury, P.B. 2016. On generalized quasi-conformal manifolds. Communication Korean Mathematics Society, 31, 163-176.
  • Calin, C., Crasmareanu, M. 2010. From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds. Bulletin of the Malaysian Mathematical Sciences Society, 33, 361-368.
  • Cortés, V. Lawn, M.A., Schäfer, L. 2006. Affine hyperspheres associated to special para-Kähler manifolds. International Journal of Geometric Methods in Modern Physic, 3, 995-1009.
  • De, U.C. Turan, M. Yıldız, A., De, A. 2012. Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds. Publicationes Mathematicae Debrecen, 80, 1-16.
  • Eisenhart, L.P. 1949. Riemannian geometry. J Princeton University Press.
  • Erdem, S. 2002. On almost (para) contact (hyperbolic) metric manifolds and harmonicity of holomorphic maps between them. Houston Journal of Mathematics, 28, 21-45.
  • Hamilton, R.S. 1982. Three-manifolds with positive Ricci curvature. Journal of Differential Geometry, 17, 301-308.
  • Hodesh, O., Fong, F.T.H. 2013. Rotational symmetry of canonical Kähler-Ricci solitons. arXiv: 1304.0277v2.
  • Ishii, Y. 1957. On conharmonic transformation. Tensor (N.S.), 7, 73-80.
  • Kaneyuki, S., Konzai, M. 1985. Paracomplex structure and affine symmetric spaces. Tokyo Journal of Mathematics, 8, 301-308.
  • Pokhariyal, G.P., Mishra, R.S. 1970. Curvature tensor and relativistics significance. Yokohama Mathematics Journal, 18, 105-108.
  • Turan, M. De, U.C., Yıldız, A. 2012. Ricci solitons and gradient Ricci solitons in 3-dimensional trans-Sasakian manifolds. Filomat, 26, 363-370.
  • Yano, K., Sawaki, S. 1968. Riemannian manifolds admitting a conformal transformation group. Journal of Differential Geometry, 2, 161-184.
  • Yano, K., Bochner, S. 1953. Curvature and Betti numbers. Annals of Mathematics Studies, 32, Princeton University Press.
  • Yüksel Perktaş, S. and Keleş, S. 2015. Ricci solitons in 3-dimensional normal almost paracontact metric manifolds. International Electronic Journal of Geometry, 8, 34-45.
  • Zamkovoy, S. 2009. Canonical connection on paracontact manifolds. Annals of Global Analysis and Geometry, 36, 37-60.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Bilal Eftal Acet

Yayımlanma Tarihi 31 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 2

Kaynak Göster

APA Acet, B. E. (2018). A Note on Ricci Solitons on Para-Sasakian Manifolds. Erzincan University Journal of Science and Technology, 11(2), 237-242. https://doi.org/10.18185/erzifbed.402310