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.
Anahtar Kelimeler
Ricci soliton semi-invariant submanifolds trans Sasakian manifold Einstein manifold
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.
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.
Anahtar Kelimeler
Ricci soliton semi-invaryant altmanifoldlar trans Sasakian manifold Einstein manifold
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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebirsel ve Diferansiyel Geometri |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Gönderilme Tarihi | 8 Ekim 2025 |
| Kabul Tarihi | 13 Ekim 2025 |
| Yayımlanma Tarihi | 19 Ekim 2025 |
| DOI | https://doi.org/10.33773/jum.1799886 |
| IZ | https://izlik.org/JA77MT26SY |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 8 Sayı: 2 |