[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).
[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
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.
[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).
[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).
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. April 2021;14(1):85-90. doi:10.36890/iejg.831078
Chicago
De, U.c., and Fatemah Mofarreh. “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”. International Electronic Journal of Geometry 14, no. 1 (April 2021): 85-90. https://doi.org/10.36890/iejg.831078.
EndNote
De U, Mofarreh F (April 1, 2021) A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds. International Electronic Journal of Geometry 14 1 85–90.
IEEE
U. De and F. Mofarreh, “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”, Int. Electron. J. Geom., vol. 14, no. 1, pp. 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 (April 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. and Fatemah Mofarreh. “A Note on Gradient Solitons in Three-Dimensional Riemannian Manifolds”. International Electronic Journal of Geometry, vol. 14, no. 1, 2021, pp. 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.