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A Note on Ricci Solitons on Para-Sasakian Manifolds

Yıl 2018, , 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, , 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

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