Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton
Yıl 2025,
Cilt: 8 Sayı: 2, 140 - 149, 19.10.2025
Ramazan Sarı
,
Süleyman Dirik
Öz
In this paper, we investigate Ricci solitions on semi-invariant submanifolds of trans Sasakian manifold. We obtain the conditions for the soliton to be steady, shrinking and expanding. We give an example for semi-invariant submanifolds of trans Sasakian manifold with ricci soliton.
Kaynakça
-
Chen, B. Y., & Deshmukh, S. (2014). Classification of Ricci solitons on Euclidean hypersurfaces. International
Journal of Mathematics, 25 (11), 1450104.
-
Chen, B. Y., & Deshmukh, S. (2014). Geometry of compact shrinking Ricci solitons. Balkan Journal of
Geometry and Its Applications, 19, 13–21.
-
Deshmukh, S., Al-Sodais, H., & Alodan, H. (2011). A note on Ricci solitons. Balkan Journal of Geometry
and Its Applications, 16, 48–55.
-
Gherghe, C. (2000). Harmonicity on nearly trans-Sasaki manifolds. Demonstratio Mathematica, 33, 151–
157.
-
Gray, A., & Hervella, L. M. (1980). The sixteen classes of almost Hermitian manifolds and their linear
invariants. Annali di Matematica Pura ed Applicata, 123 (4), 35–58.
-
Hamilton, R. S. (1988). The Ricci flow on surfaces. Mathematics and General Relativity (Contemporary
Mathematics, 71), 237–262.
-
Hui, S. K., Lemence, R. S., & Chakraborty, D. (2015). Ricci solitons on three dimensional generalized
Sasakian space-forms. Tensor (N. S.), 76, 75–83.
-
Ingalahalli, G., & Bagewadi, C. (2012). Ricci solitons in α-Sasakian manifolds. ISRN Geometry, 1–13.
-
Marrero, J. C. (1992). The local structure of trans-Sasakian manifolds. Annali di Matematica Pura ed
Applicata, 162 (4), 77–86.
-
Morgan, J. W., & Tian, G. (2007). Ricci flow and the Poincaré conjecture. American Mathematical
Society.
-
Nagaraja, H. G., & Premalatta, C. R. (2012). Ricci solitons in Kenmotsu manifolds. Journal of Mathematical
Analysis, 3 (2), 18–24.
-
Oubina, J. A. (1985). New classes of almost contact metric structures. Publicationes Mathematicae
Debrecen, 32, 187–193. (Not: Sayfa aralığı 197-193, 187-193 olarak düzeltildi.)
-
Turgut Vanlı, A., & Sarı, R. (2010). On invariant submanifolds of trans-Sasakian manifolds. Differential Geometry -Dynamical Systems, 12, 277–288.
Ricci solitonlu Trans Sasakian Manifoldun Semi-İnvaryant Altmanifoldları
Yıl 2025,
Cilt: 8 Sayı: 2, 140 - 149, 19.10.2025
Ramazan Sarı
,
Süleyman Dirik
Öz
Bu makalede, trans Sasakian manifoldunun sem-invaryant alt manifoldları üzerinde Ricci solitonu araştırıyoruz. Solitonun sabit, küçülme ve genişleme koşullarını elde ediyoruz. Ricci solitonu olan trans Sasakian manifoldunun semi-invaryant alt manifoldları için bir örnek veriyoruz.
Kaynakça
-
Chen, B. Y., & Deshmukh, S. (2014). Classification of Ricci solitons on Euclidean hypersurfaces. International
Journal of Mathematics, 25 (11), 1450104.
-
Chen, B. Y., & Deshmukh, S. (2014). Geometry of compact shrinking Ricci solitons. Balkan Journal of
Geometry and Its Applications, 19, 13–21.
-
Deshmukh, S., Al-Sodais, H., & Alodan, H. (2011). A note on Ricci solitons. Balkan Journal of Geometry
and Its Applications, 16, 48–55.
-
Gherghe, C. (2000). Harmonicity on nearly trans-Sasaki manifolds. Demonstratio Mathematica, 33, 151–
157.
-
Gray, A., & Hervella, L. M. (1980). The sixteen classes of almost Hermitian manifolds and their linear
invariants. Annali di Matematica Pura ed Applicata, 123 (4), 35–58.
-
Hamilton, R. S. (1988). The Ricci flow on surfaces. Mathematics and General Relativity (Contemporary
Mathematics, 71), 237–262.
-
Hui, S. K., Lemence, R. S., & Chakraborty, D. (2015). Ricci solitons on three dimensional generalized
Sasakian space-forms. Tensor (N. S.), 76, 75–83.
-
Ingalahalli, G., & Bagewadi, C. (2012). Ricci solitons in α-Sasakian manifolds. ISRN Geometry, 1–13.
-
Marrero, J. C. (1992). The local structure of trans-Sasakian manifolds. Annali di Matematica Pura ed
Applicata, 162 (4), 77–86.
-
Morgan, J. W., & Tian, G. (2007). Ricci flow and the Poincaré conjecture. American Mathematical
Society.
-
Nagaraja, H. G., & Premalatta, C. R. (2012). Ricci solitons in Kenmotsu manifolds. Journal of Mathematical
Analysis, 3 (2), 18–24.
-
Oubina, J. A. (1985). New classes of almost contact metric structures. Publicationes Mathematicae
Debrecen, 32, 187–193. (Not: Sayfa aralığı 197-193, 187-193 olarak düzeltildi.)
-
Turgut Vanlı, A., & Sarı, R. (2010). On invariant submanifolds of trans-Sasakian manifolds. Differential Geometry -Dynamical Systems, 12, 277–288.