SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 4

Gradient Weyl-Ricci Soliton

Cornelıa-lıvıa BEJAN
Şemsi Eken MERİÇ
Erol KILIÇ
Pages
1137–1145
Publication Date
2020-08-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton.
📊
Key Findings & Data:A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric.
💡
Conclusion & Impact:We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Weyl structure · Ricci soliton · Sasaki metric

Abstract

The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.

🔖

Cite This Article

BEJAN, C., MERİÇ, Ş. E., KILIÇ, E. (2020). Gradient Weyl-Ricci Soliton. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 4, 1137–1145. https://ajindex.com/articles/185507

References (3)

  1. Abbassi MTK, Sarih M. On Riemannian g-natural metrics of the form a.gs + b.gh + c.gv on the tangent bundle of a Riemannian manifold (M, g). Mediterranean Journal of Mathematics 2005; 2 (1): 19-43. doi:10.1007/s00009-005- 0028-8 [2] Abbassi MTK, Sarih M. On some herditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds. Differential Geometry and its Applications 2005; 22 (1): 19-47. doi.org/10.1016/j.difgeo.2004.07.003 [3] Bejan CL, Chiriac NC. Weyl structures on almost paracontact manifolds. International Journal of Geometric Methods and Modern Physics 2013; 10 (1): 1220019 (9 pages). doi.org/10.1142/S0219887812200198 [4] Bejan CL, Crasmareanu M. Weakly-symmetry of the Sasakian lifts on tangent bundles. Publicationes Mathematicae Debrecen, 2013; 83, 1-2 (4): 63-69. [5] Bejan CL, Druta-Romaniuc SL. Connections which are harmonic with respect to general natural metrics. Differential Geometry and its Applications 2012; 30 (4): 306-317. doi.org/10.1016/j.difgeo.2012.05.004 [6] Bejan CL, Gül İ. Sasaki metric on the tangent bundle of a Weyl manifold. Publications de I’Institut Mathematique (Beograd) (N.S.) 2018; 103 (117): 25-32. doi.org/10.2298/PIM1817025B [7] Calderbank D, Pedersen H. Einstein-Weyl geometry; in: Essays on Einstein manifolds (LeBrun and Wang editors). Surveys in Differential Geometry 2001; 6: 387-423. doi: 10.4310/SDG.2001.v6.n1.a14 [8] Folland G. Weyl manifold. Journal of Differential Geometry 1970; 4 (2): 145-153. doi:10.4310/jdg/1214429379 [9] Hamilton RS. The Formation of Singularities in the Ricci Flow. Surveys in Differential Geometry, Vol. II (Cambridge, MA, 1993) 7–136,
  2. International Press,
  3. Cambridge, MA, 1995. [10] Janyska J. Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold. Archivum Mathematicum (Brno) 2001; 37 (2): 143-160. doi: 10338.dmlcz/107794 [11] Kowalski O, Sekizawa M. Natural transformations of Riemannian metrics on manifolds to metrics on the tangent bundles-a classification. Bulletin of Tokyo Gakugei University 1988; 40 (4): 1-29. [12] Lee SD, Kim BH, Choi JH. Warped product spaces with Ricci conditions. Turkish Journal of Mathematics 2017; 41 (6): 1365-1375. doi: 10.3906/mat-1606-49 [13] Oproiu V, Papaghiuc N. General natural Einstein Kähler structures on tangent bundles. Differential Geometry and its Applications 2009; 27 (3): 384-392. doi.org/10.1016/j.difgeo.2008.10.017 [14] Sasaki S. On the differential geometry of tangent bundles