Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton

Abstract

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.

Keywords

• Ricci soliton
• semi-invariant submanifolds
• trans Sasakian manifold
• Einstein manifold

Ricci solitonlu Trans Sasakian Manifoldun Semi-İnvaryant Altmanifoldları

Abstract

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.

Keywords

• Ricci soliton
• semi-invaryant altmanifoldlar
• trans Sasakian manifold
• Einstein manifold

References

1. Chen, B. Y., & Deshmukh, S. (2014). Classification of Ricci solitons on Euclidean hypersurfaces. International Journal of Mathematics, 25 (11), 1450104.
2. Chen, B. Y., & Deshmukh, S. (2014). Geometry of compact shrinking Ricci solitons. Balkan Journal of Geometry and Its Applications, 19, 13–21.
3. Deshmukh, S., Al-Sodais, H., & Alodan, H. (2011). A note on Ricci solitons. Balkan Journal of Geometry and Its Applications, 16, 48–55.
4. Gherghe, C. (2000). Harmonicity on nearly trans-Sasaki manifolds. Demonstratio Mathematica, 33, 151– 157.
5. 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.
6. Hamilton, R. S. (1988). The Ricci flow on surfaces. Mathematics and General Relativity (Contemporary Mathematics, 71), 237–262.
7. Hui, S. K., Lemence, R. S., & Chakraborty, D. (2015). Ricci solitons on three dimensional generalized Sasakian space-forms. Tensor (N. S.), 76, 75–83.
8. Ingalahalli, G., & Bagewadi, C. (2012). Ricci solitons in α-Sasakian manifolds. ISRN Geometry, 1–13.

9. Marrero, J. C. (1992). The local structure of trans-Sasakian manifolds. Annali di Matematica Pura ed Applicata, 162 (4), 77–86.
10. Morgan, J. W., & Tian, G. (2007). Ricci flow and the Poincaré conjecture. American Mathematical Society.
11. Nagaraja, H. G., & Premalatta, C. R. (2012). Ricci solitons in Kenmotsu manifolds. Journal of Mathematical Analysis, 3 (2), 18–24.
12. 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.)
13. Turgut Vanlı, A., & Sarı, R. (2010). On invariant submanifolds of trans-Sasakian manifolds. Differential Geometry -Dynamical Systems, 12, 277–288.