Research Article
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Year 2019, , 157 - 168, 03.10.2019
https://doi.org/10.36890/iejg.628073

Abstract

References

  • [1] Barbosa, E. and Ribeiro, E., On conformal solutions of the yamabe flow. Archiv der Mathematik 101 (2013), 79-89.
  • [2] Cao, H-D., Sun, X. and Zhang, Y., On the structure of gradient yamabe solitons. Mathematical Research Letters 19 (2012), 767-774.
  • [3] De, U. C., Turan, M., Yıldız, A. and De, A., Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds. Publicationes Mathematica Debrecen 80 (2012), 127-142.
  • [4] Dobarro, F. and Ünal, B., Curvature of multiply warped products. Journal of Geometry and Physics 55 (2005), 75-106.
  • [5] Feitosa, F. E. S., Freitas, A. A. and Gomes, J. N. V., On the construction of gradient Ricci soliton warped product. Nonlinear Analysis 161 (2017), 30-43.
  • [6] He, C., Petersen, P. and Wylie, W., Warped product rigidity. Asian J. Math. 19 (2015), 135-170. [7] He, C., Gradient Yamabe solitons on warped products. arXiv preprint arXiv:1109.2343, (2011).
  • [8] Karaca, F. and Özgür, C., Gradient Ricci Solitons on Multiply Warped Product Manifolds. Filomat 32 (2018), 4221-4228.
  • [9] Lee, S. D., Kim, B. H. and Choi, J. H., On a classification of warped product spaces with gradient Ricci solitons. The Korean Journal of Mathematics 24 (2016), 627-636.
  • [10] Lee, S. D., Kim, B. H. and Choi, J. H., Warped product spaces with Ricci conditions. Turkish Journal of Mathematics 41 (2017), 1365-1375.
  • [11] Ma, L. and Miquel, V., Remarks on scalar curvature of Yamabe solitons. Annals of Global Analysis and Geometry 42 (2012), 195-205.
  • [12] Neto, B. L. and Tenenblat, K., On gradient yamabe solitons conformal to a pseudoeuclidian space. Journal of Geometry and Physics 123 (2018), 284-291.
  • [13] Sousa, M. L. and Pina, R., Gradient ricci solitons with structure of warped product. Results in Mathematics 71(3-4) (2017), 825-840.
  • [14] Ünal, B., Doubly warped products. Ph.D. Thesis, University of Missouri-Columbia, 2000.
  • [15] Ünal, B., Multiply warped products. Journal of Geometry and Physics 34 (2000), 287-301.
  • [16] Tokura, W., Adriano, L., Pina, R. and Barboza, M., On warped product gradient Yamabe solitons. Journal of Mathematical Analysis and Applications 473(1) (2019), 201-214.
  • [17] Turan, M., De, U. C. and Yıldız, A., Ricci solitons and gradient Ricci solitons in three-dimensional trans-Sasakian manifolds. Filomat 26(2) (2012), 363-370.

Gradient Yamabe Solitons on Multiply Warped Product Manifolds

Year 2019, , 157 - 168, 03.10.2019
https://doi.org/10.36890/iejg.628073

Abstract

We consider gradient Yamabe solitons on multiply warped product manifolds. We find the
necessary and sufficient conditions for multiply warped product manifolds to be gradient Yamabe
solitons.

References

  • [1] Barbosa, E. and Ribeiro, E., On conformal solutions of the yamabe flow. Archiv der Mathematik 101 (2013), 79-89.
  • [2] Cao, H-D., Sun, X. and Zhang, Y., On the structure of gradient yamabe solitons. Mathematical Research Letters 19 (2012), 767-774.
  • [3] De, U. C., Turan, M., Yıldız, A. and De, A., Ricci solitons and gradient Ricci solitons on 3-dimensional normal almost contact metric manifolds. Publicationes Mathematica Debrecen 80 (2012), 127-142.
  • [4] Dobarro, F. and Ünal, B., Curvature of multiply warped products. Journal of Geometry and Physics 55 (2005), 75-106.
  • [5] Feitosa, F. E. S., Freitas, A. A. and Gomes, J. N. V., On the construction of gradient Ricci soliton warped product. Nonlinear Analysis 161 (2017), 30-43.
  • [6] He, C., Petersen, P. and Wylie, W., Warped product rigidity. Asian J. Math. 19 (2015), 135-170. [7] He, C., Gradient Yamabe solitons on warped products. arXiv preprint arXiv:1109.2343, (2011).
  • [8] Karaca, F. and Özgür, C., Gradient Ricci Solitons on Multiply Warped Product Manifolds. Filomat 32 (2018), 4221-4228.
  • [9] Lee, S. D., Kim, B. H. and Choi, J. H., On a classification of warped product spaces with gradient Ricci solitons. The Korean Journal of Mathematics 24 (2016), 627-636.
  • [10] Lee, S. D., Kim, B. H. and Choi, J. H., Warped product spaces with Ricci conditions. Turkish Journal of Mathematics 41 (2017), 1365-1375.
  • [11] Ma, L. and Miquel, V., Remarks on scalar curvature of Yamabe solitons. Annals of Global Analysis and Geometry 42 (2012), 195-205.
  • [12] Neto, B. L. and Tenenblat, K., On gradient yamabe solitons conformal to a pseudoeuclidian space. Journal of Geometry and Physics 123 (2018), 284-291.
  • [13] Sousa, M. L. and Pina, R., Gradient ricci solitons with structure of warped product. Results in Mathematics 71(3-4) (2017), 825-840.
  • [14] Ünal, B., Doubly warped products. Ph.D. Thesis, University of Missouri-Columbia, 2000.
  • [15] Ünal, B., Multiply warped products. Journal of Geometry and Physics 34 (2000), 287-301.
  • [16] Tokura, W., Adriano, L., Pina, R. and Barboza, M., On warped product gradient Yamabe solitons. Journal of Mathematical Analysis and Applications 473(1) (2019), 201-214.
  • [17] Turan, M., De, U. C. and Yıldız, A., Ricci solitons and gradient Ricci solitons in three-dimensional trans-Sasakian manifolds. Filomat 26(2) (2012), 363-370.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Fatma Karaca This is me

Publication Date October 3, 2019
Published in Issue Year 2019

Cite

APA Karaca, F. (2019). Gradient Yamabe Solitons on Multiply Warped Product Manifolds. International Electronic Journal of Geometry, 12(2), 157-168. https://doi.org/10.36890/iejg.628073
AMA Karaca F. Gradient Yamabe Solitons on Multiply Warped Product Manifolds. Int. Electron. J. Geom. October 2019;12(2):157-168. doi:10.36890/iejg.628073
Chicago Karaca, Fatma. “Gradient Yamabe Solitons on Multiply Warped Product Manifolds”. International Electronic Journal of Geometry 12, no. 2 (October 2019): 157-68. https://doi.org/10.36890/iejg.628073.
EndNote Karaca F (October 1, 2019) Gradient Yamabe Solitons on Multiply Warped Product Manifolds. International Electronic Journal of Geometry 12 2 157–168.
IEEE F. Karaca, “Gradient Yamabe Solitons on Multiply Warped Product Manifolds”, Int. Electron. J. Geom., vol. 12, no. 2, pp. 157–168, 2019, doi: 10.36890/iejg.628073.
ISNAD Karaca, Fatma. “Gradient Yamabe Solitons on Multiply Warped Product Manifolds”. International Electronic Journal of Geometry 12/2 (October 2019), 157-168. https://doi.org/10.36890/iejg.628073.
JAMA Karaca F. Gradient Yamabe Solitons on Multiply Warped Product Manifolds. Int. Electron. J. Geom. 2019;12:157–168.
MLA Karaca, Fatma. “Gradient Yamabe Solitons on Multiply Warped Product Manifolds”. International Electronic Journal of Geometry, vol. 12, no. 2, 2019, pp. 157-68, doi:10.36890/iejg.628073.
Vancouver Karaca F. Gradient Yamabe Solitons on Multiply Warped Product Manifolds. Int. Electron. J. Geom. 2019;12(2):157-68.