A study on Kenmotsu Ricci soliton manifolds

Yıl 2025, Cilt: 8 Sayı: 2, 150 - 159, 19.10.2025

İnan Ünal

https://doi.org/10.33773/jum.1804823

Öz

In this paper, we study Ricci solitons on Kenmotsu manifolds with respect to generalized Tanaka-Webster connection. We obtain some results on a type of Ricci solitons related to potential vector field under certain curvature conditions. Also, we use the results on the Kenmotsu manifolds with respect to generalized Tanaka-Webster connection in the literature and we classify Ricci solitons with special conditions.

Anahtar Kelimeler

Ricci soliton , Kenmotsu manifold , Tanaka-Webster connection

Kenmotsu Ricci Soliton Manifoldları Üzerine Bir Çalışma

Öz

Bu çalışmada, Kenmotsu manifoldları üzerinde Ricci solitonlarını genelleştirilmiş Tanaka-Webster bağlantısına göre inceliyoruz. Belirli eğrilik koşulları altında potansiyel vektör alanı ile ilgili bir Ricci soliton türü hakkında bazı sonuçlar elde ettik. Ayrıca, literatürdeki genelleştirilmiş Tanaka-Webster bağlantısına göre Kenmotsu manifoldları ile ilgili sonuçları kullanıyoruz ve Ricci solitonlarını özel koşullarla sınıflandırıyoruz.

Anahtar Kelimeler

Ricci soliton , Kenmotsu manifold , Tanaka-Webster connection

Kaynakça

• Hamilton, R. (1988). The Ricci flow on surfaces. Contemporary Mathematics, 71, 237–261.
• Hamilton, R. (1995). The formation of singularities in the Ricci flow. Surveys in Differential Geometry, 2, 7–136.
• Sharma, R. (2008). Certain results on K-contact and (κ, μ)-contact manifolds. Journal of Geometry, 89, 138–147.
• Cho, J. T. (2013). Almost contact 3-manifolds and Ricci solitons. International Journal of Geometric Methods in Modern Physics, 10(1), 1220022.
• Cho, J. T., & Sharma, R. (2010). Contact geometry and Ricci solitons. International Journal of Geometric Methods in Modern Physics, 7(6), 951–960.
• Crasmareanu, M. (2012). Parallel tensors and Ricci solitons in N(κ)-quasi Einstein manifolds. Indian Journal of Pure and Applied Mathematics, 43, 359–369.
• Ghosh, A., & Sharma, R. (2012). K-contact metrics as Ricci solitons. Beiträge zur Algebra und Geometrie, 53, 25–30.
• Ghosh, A., & Sharma, R. (2013). Sasakian metric as a Ricci soliton and related results. Journal of Geometry and Physics, 75, 1–6.
• Ghosh, A., & Patra, D. S. (2018). The k-almost Ricci solitons and contact geometry. Journal of the Korean Mathematical Society, 55(1), 161–174.
• Venkatesha, V., & Aruna Kumara, H. (2019). Ricci soliton and geometrical structures in a perfect fluid spacetime with torse-forming vector field. Afrika Matematika, 30, 725–736.
• Tripathi, M. M. (2008). Ricci solitons on contact manifolds. arXiv preprint arXiv:0801.4222.
• Kenmotsu, K. (1972). A class of almost contact Riemannian manifolds. Tohoku Mathematical Journal, 24, 93–103.
• Pitiş, G. (2007). Geometry of Kenmotsu Manifolds. Transilvania University Press.
• Ghosh, A. (2011). Kenmotsu 3-metric as a Ricci soliton. Chaos, Solitons and Fractals, 44, 647–650.
• Ghosh, A. (2013). An η-Einstein Kenmotsu metric as a Ricci soliton. Publications Mathematicae Debrecen, 82(3–4), 591–598.
• Ghosh, A. (2019). Ricci solitons and Ricci almost solitons within the framework of Kenmotsu manifolds. Carpathian Mathematical Publications, 11(1), 59–69.
• Ayar, G., & Yıldırım, M. (2019). Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds. Facta Universitatis, Series: Mathematics and Informatics, 34(3), 503–510.
• Hui, S. K., Prasad, R., & Chakraborty, D. (2017). Ricci solitons on Kenmotsu manifolds with respect to quarter-symmetric non-metric ϕ-connection. Ganita, 67, 195–204.
• Nagaraja, H. G., & Kiran Kumar, D. L. (2019). Ricci solitons in Kenmotsu manifolds under generalized D-conformal deformation. Lobachevskii Journal of Mathematics, 40(2), 195–200.
• Bagewadi, C. S., Ingalahalli, G., & Ashoka, S. R. (2013). A study on Ricci solitons in Kenmotsu manifolds. International Scholarly Research Notices, 2013, Article ID 243256.
• Nagaraja, H. G., & Venu, K. (2016). Ricci solution in Kenmotsu manifolds. Journal of Informatics and Mathematical Sciences, 8(1), 29–36.
• Ayar, G., & Demirhan, D. (2019). Ricci solitons on nearly Kenmotsu manifolds with semi-symmetric metric connection. Journal of Engineering Technology and Applied Sciences, 4(3), 131–140.
• Tanaka, N. (1976). On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections. Japanese Journal of Mathematics, New Series, 2(1), 131–190.
• Webster, S. M. (1978). Pseudo-Hermitian structures on a real hypersurface. Journal of Differential Geometry, 13(1), 25–41.
• Tanno, S. (1989). Variational problems on contact Riemannian manifolds. Transactions of the American Mathematical Society, 314(1), 349–379.
• Ünal, İ., & Altın, M. (2021). N(κ)-contact metric manifolds with generalized Tanaka–Webster connection. Filomat, 35(4), 1383–1392.
• De, U. C., & Ghosh, G. (2016). On generalized Tanaka–Webster connection in Sasakian manifolds. Bulletin of the Transilvania University of Braşov, 9(2), 13–24.
• Montano, B. C. (2010). Some remarks on the generalized Tanaka–Webster connection of a contact metric manifold. Rocky Mountain Journal of Mathematics, 40, 1009–1037.
• Kazan, A., & Karadağ, H. B. (2018). Trans-Sasakian manifolds with respect to generalized Tanaka–Webster connection. Honam Mathematical Journal, 40(3), 487–508.
• Mocanu, R. (2009). Gray curvature conditions and the Tanaka–Webster connection. In Differential Geometry: Proceedings of the VIII International Colloquium, Santiago de Compostela, Spain, 7–11 July 2008 (p. 291). World Scientific.
• Perktaş, S. Y., Acet, B. E., & Kılıç, E. (2013). Kenmotsu manifolds with generalized Tanaka–Webster connection. Adıyaman University Journal of Science, 3(2), 79–93.
• Ghosh, G., & De, U. C. (2017). Kenmotsu manifolds with generalized Tanaka–Webster connection. Publications de l’Institut Mathématique, 102(116), 221–230.
• Prakasha, D. G., & Hadimani, B. S. (2018). On the conharmonic curvature tensor of Kenmotsu manifolds with generalized Tanaka–Webster connection. Miskolc Mathematical Notes, 19(1), 491–503.
• Kiran Kumar, D. L., Nagaraja, H. G., & Kumari, D. (2019). Concircular curvature tensor of Kenmotsu manifolds admitting generalized Tanaka–Webster connection. Journal of Mathematics and Computer Science, 9(4), 447–462.
• Blair, D. E. (2010). Riemannian Geometry of Contact and Symplectic Manifolds. Birkhäuser.
• Ahsan, Z. (2015). Tensors, Mathematics of Differential Geometry and Relativity. PHI Learning Private Limited.