Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2025, Cilt: 8 Sayı: 2, 140 - 149, 19.10.2025
https://doi.org/10.33773/jum.1799886

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
https://doi.org/10.33773/jum.1799886

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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Araştırma Makalesi
Yazarlar

Ramazan Sarı 0000-0002-4618-8243

Süleyman Dirik 0000-0001-9093-1607

Yayımlanma Tarihi 19 Ekim 2025
Gönderilme Tarihi 8 Ekim 2025
Kabul Tarihi 13 Ekim 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 2

Kaynak Göster

APA Sarı, R., & Dirik, S. (2025). Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton. Journal of Universal Mathematics, 8(2), 140-149. https://doi.org/10.33773/jum.1799886
AMA Sarı R, Dirik S. Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton. JUM. Ekim 2025;8(2):140-149. doi:10.33773/jum.1799886
Chicago Sarı, Ramazan, ve Süleyman Dirik. “Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton”. Journal of Universal Mathematics 8, sy. 2 (Ekim 2025): 140-49. https://doi.org/10.33773/jum.1799886.
EndNote Sarı R, Dirik S (01 Ekim 2025) Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton. Journal of Universal Mathematics 8 2 140–149.
IEEE R. Sarı ve S. Dirik, “Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton”, JUM, c. 8, sy. 2, ss. 140–149, 2025, doi: 10.33773/jum.1799886.
ISNAD Sarı, Ramazan - Dirik, Süleyman. “Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton”. Journal of Universal Mathematics 8/2 (Ekim2025), 140-149. https://doi.org/10.33773/jum.1799886.
JAMA Sarı R, Dirik S. Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton. JUM. 2025;8:140–149.
MLA Sarı, Ramazan ve Süleyman Dirik. “Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton”. Journal of Universal Mathematics, c. 8, sy. 2, 2025, ss. 140-9, doi:10.33773/jum.1799886.
Vancouver Sarı R, Dirik S. Semi-Invariant Submanifolds of a Trans Sasakian Manifold with Ricci Soliton. JUM. 2025;8(2):140-9.