Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 14 Sayı: 1, 85 - 90, 15.04.2021
https://doi.org/10.36890/iejg.831078

Öz

Kaynakça

  • [1] Blaga, A. M.: On gradient eta-Einstein solitons. Kragujevac Journal of Mathematics. 42, 229-237 (2018).
  • [2] Blaga, A. M.: Some geometrical aspects of Einstein, Ricci and Yamabe solitons. J. Geom. Sym. Physics. 52, 17-26 (2019).
  • [3] Blaga, A. M. and Ozgur, C.: Almost eta-Ricci and almost eta-Yamabe solitons with torse-forming potential vector field. Quaestiones Mathematicae. https://doi.org/10.2989/16073606.2020.1850538
  • [4] Cao, H. D., Sun, X. F. and Zhang, Y. Y.: On the structure of gradient Yamabe solitons. Mathematical Research Letters. 19, 737-774 (2002).
  • [5] Catino, G., Mazzieri, L.: Gradient Einstein soliton. Nonlinear Anal., 132, 66-94 (2016).
  • [6] Chen, B.Y. and Deshmukh S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15, 194 (2018).
  • [7] De, U.C., Chaubey, S.K. and Suh, Y.J.: A note on almost co-Kahler manifolds. Int. J. of Geo. Methods in Modern Phy. 17 (10), 2050153 (2020).
  • [8] Desmukh, S. and Chen, B. Y.: A note on Yamabe solitons. Balk. J. Geo. Appl. 23, 37-43 (2018).
  • [9] Hamilton, R.S.: The Ricci flow on surfaces. Mathematics and general Relativity, Contemp. Math. 71, 237-262(1998).
  • [10] Hsu, S.Y.: A note on compact gradient Yamabe solitons. J. Math. Ana. Appl. 388, 725-726 (2012).
  • [11] Karaca, F.: Gradient Yamabe solitons on Multiply Warped product Manifolds. Int. Electronic J. Geom. 12, 157-168 (2019).
  • [12] Karatsobanis, J. N. and Xenos, P. J.: On the new class of contact metric 3-manifolds. J. Geom. 80, 136-153 (2004).
  • [13] Koufogiorgos, T.: On a class of contact Riemannian 3-manifolds. Results in Math. 27, 51-62 (1995).
  • [14] Kowalski, O.: An explicit classification of 3-dimensional Riemannian spaces satisfying R(X; Y ):R = 0. Czechoslovak Math. J. 46(121), 427-474 (1996).
  • [15] Suh, Y.J. and De, U.C.: Yamabe solitons and gradient Yamabe solitons on three-dimensional N(k)-contact manifolds. Int. J. Geom. Methods Mod. Phys. 17 (12) 2050177, 10 pp. (2020).
  • [16] Thurston, W. P. and Winkelnkemper, H. E.: On the existence of contact forms. Proc. Amer. Math. Soc. 52, 345-347 (1975).
  • [17] Trudinger, N. S.: Remarks concerning the conformal deformation of Riemannian structures on compact manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3. 22, 265-274 (1968).
  • [18] Wang, Y.: Yamabe soliton on 3-dimensional Kenmotsu manifolds. Bull. Belg. Math. Soc. Simon Stevin. 23, 345-355 (2016).
  • [19] Yamabe, H.: On a deformation of Riemannian structures on compact manifolds. Osaka Math. J. 12 21-37 (1960).

A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds

Yıl 2021, Cilt: 14 Sayı: 1, 85 - 90, 15.04.2021
https://doi.org/10.36890/iejg.831078

Öz

We charecterize three-dimensional Riemannian manifolds endowed with a special type of vector field if the Riemannian metrices are gradient Yamabe solitons and gradient Einstein solitons respectively.

Kaynakça

  • [1] Blaga, A. M.: On gradient eta-Einstein solitons. Kragujevac Journal of Mathematics. 42, 229-237 (2018).
  • [2] Blaga, A. M.: Some geometrical aspects of Einstein, Ricci and Yamabe solitons. J. Geom. Sym. Physics. 52, 17-26 (2019).
  • [3] Blaga, A. M. and Ozgur, C.: Almost eta-Ricci and almost eta-Yamabe solitons with torse-forming potential vector field. Quaestiones Mathematicae. https://doi.org/10.2989/16073606.2020.1850538
  • [4] Cao, H. D., Sun, X. F. and Zhang, Y. Y.: On the structure of gradient Yamabe solitons. Mathematical Research Letters. 19, 737-774 (2002).
  • [5] Catino, G., Mazzieri, L.: Gradient Einstein soliton. Nonlinear Anal., 132, 66-94 (2016).
  • [6] Chen, B.Y. and Deshmukh S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15, 194 (2018).
  • [7] De, U.C., Chaubey, S.K. and Suh, Y.J.: A note on almost co-Kahler manifolds. Int. J. of Geo. Methods in Modern Phy. 17 (10), 2050153 (2020).
  • [8] Desmukh, S. and Chen, B. Y.: A note on Yamabe solitons. Balk. J. Geo. Appl. 23, 37-43 (2018).
  • [9] Hamilton, R.S.: The Ricci flow on surfaces. Mathematics and general Relativity, Contemp. Math. 71, 237-262(1998).
  • [10] Hsu, S.Y.: A note on compact gradient Yamabe solitons. J. Math. Ana. Appl. 388, 725-726 (2012).
  • [11] Karaca, F.: Gradient Yamabe solitons on Multiply Warped product Manifolds. Int. Electronic J. Geom. 12, 157-168 (2019).
  • [12] Karatsobanis, J. N. and Xenos, P. J.: On the new class of contact metric 3-manifolds. J. Geom. 80, 136-153 (2004).
  • [13] Koufogiorgos, T.: On a class of contact Riemannian 3-manifolds. Results in Math. 27, 51-62 (1995).
  • [14] Kowalski, O.: An explicit classification of 3-dimensional Riemannian spaces satisfying R(X; Y ):R = 0. Czechoslovak Math. J. 46(121), 427-474 (1996).
  • [15] Suh, Y.J. and De, U.C.: Yamabe solitons and gradient Yamabe solitons on three-dimensional N(k)-contact manifolds. Int. J. Geom. Methods Mod. Phys. 17 (12) 2050177, 10 pp. (2020).
  • [16] Thurston, W. P. and Winkelnkemper, H. E.: On the existence of contact forms. Proc. Amer. Math. Soc. 52, 345-347 (1975).
  • [17] Trudinger, N. S.: Remarks concerning the conformal deformation of Riemannian structures on compact manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 3. 22, 265-274 (1968).
  • [18] Wang, Y.: Yamabe soliton on 3-dimensional Kenmotsu manifolds. Bull. Belg. Math. Soc. Simon Stevin. 23, 345-355 (2016).
  • [19] Yamabe, H.: On a deformation of Riemannian structures on compact manifolds. Osaka Math. J. 12 21-37 (1960).
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

U.c. De 0000-0002-8990-4609

Fatemah Mofarreh 0000-0002-2116-7382

Yayımlanma Tarihi 15 Nisan 2021
Kabul Tarihi 3 Mart 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 14 Sayı: 1

Kaynak Göster

APA De, U., & Mofarreh, F. (2021). A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. International Electronic Journal of Geometry, 14(1), 85-90. https://doi.org/10.36890/iejg.831078
AMA De U, Mofarreh F. A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. Int. Electron. J. Geom. Nisan 2021;14(1):85-90. doi:10.36890/iejg.831078
Chicago De, U.c., ve Fatemah Mofarreh. “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”. International Electronic Journal of Geometry 14, sy. 1 (Nisan 2021): 85-90. https://doi.org/10.36890/iejg.831078.
EndNote De U, Mofarreh F (01 Nisan 2021) A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. International Electronic Journal of Geometry 14 1 85–90.
IEEE U. De ve F. Mofarreh, “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”, Int. Electron. J. Geom., c. 14, sy. 1, ss. 85–90, 2021, doi: 10.36890/iejg.831078.
ISNAD De, U.c. - Mofarreh, Fatemah. “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”. International Electronic Journal of Geometry 14/1 (Nisan 2021), 85-90. https://doi.org/10.36890/iejg.831078.
JAMA De U, Mofarreh F. A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. Int. Electron. J. Geom. 2021;14:85–90.
MLA De, U.c. ve Fatemah Mofarreh. “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”. International Electronic Journal of Geometry, c. 14, sy. 1, 2021, ss. 85-90, doi:10.36890/iejg.831078.
Vancouver De U, Mofarreh F. A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. Int. Electron. J. Geom. 2021;14(1):85-90.

Cited By

3-Dimensional f-Kenmotsu manifolds and solitons
International Journal of Geometric Methods in Modern Physics
https://doi.org/10.1142/S0219887822501997