KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 4

On locally $\phi$-semisymmetric Sasakian manifolds

Absos Ali Shaikh0000-0001-6312-2564
Chandan Kumar Mondal0000-0002-3485-9193
Helaluddin Ahmad0000-0003-2289-9996
Sayfa
—
Yayın Tarihi
2019-08-08
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is also shown that local conformal $\phi$-semisymmetry and local conharmonical $\phi$-semisymmetry are equivalent.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Generalizing the notion of local $\phi$-symmetry of Takahashi [Sasakian $\phi$-symmetric spaces, Tohoku Math.
📊
Temel Bulgular & Veri:J., 1977], in the present paper, we introduce the notion of \textit{local $\phi$-semisymmetry} of a Sasakian manifold along with its proper existence and characterization.
💡
Sonuç & Katkı:It is also shown that local conformal $\phi$-semisymmetry and local conharmonical $\phi$-semisymmetry are equivalent.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Sasakian manifold · locally $\phi$-symmetric · $\phi$-semisymmetric

Abstract

Generalizing the notion of local $\phi$-symmetry of Takahashi [Sasakian $\phi$-symmetric spaces, Tohoku Math. J., 1977], in the present paper, we introduce the notion of \textit{local $\phi$-semisymmetry} of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $\phi$-semisymmetry of a Sasakian manifold and obtain its characterization. It is shown that the local $\phi$-semisymmetry, local projective $\phi$-semisymmetry and local concircular $\phi$-semisymmetry are equivalent. It is also shown that local conformal $\phi$-semisymmetry and local conharmonical $\phi$-semisymmetry are equivalent.

🔖

Bu Makaleye Atıf Yap

Shaikh, A. A., Mondal, C. K., Ahmad, H. (2019). On locally $\phi$-semisymmetric Sasakian manifolds. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 4. https://ajindex.com/articles/1402771

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (23)

  1. D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math., Springer-Verlag, 1976.
  2. É. Cartan, Sur une classe remarquable déspaces de Riemann, I, Bull. de la Soc. Math. de France 54, 214-216, 1926.
  3. É. Cartan, Sur une classe remarquable déspaces de Riemann, II, Bull. de la Soc. Math. de France 55, 114-134, 1927.
  4. É. Cartan, Lecons sur la geometrie des espaces de Riemann, 2nd ed., Paris, 1946.
  5. M.C. Chaki and M. Tarafdar, On a type of Sasakian manifold, Soochow J. Math. 16, 23-28, 1990.
  6. U.C. De, A.A. Shaikh and S. Biswas, On $\phi$-recurrent Sasakian manifolds, Novi Sad J. Math. 33(2), 43-48, 2003.
  7. K. Ogiue, On fiberings of almost contact manifolds, Kodai Math. Sem. Rep. 17, 53-62, 1965.
  8. A.A. Shaikh and K.K. Baishya, On $\phi$-symmetric LP-Sasakian manifolds, Yokohama Math. J. 52, 97-112, 2005.
  9. A.A. Shaikh, K.K. Baishya and S. Eyasmin, On $\phi$-recurrent generalized $(k, \mu)$-contact metric manifolds, Lobachevski J. Math. 27, 3-13, 2007.
  10. A.A. Shaikh, K.K. Baishya and S. Eyasmin, On the existence of some types of LP-Sasakian manifolds, Commun. Korean Math. Soc., 23 (1), 1-16, 2008.
  11. A.A. Shaikh, T. Basu and S. Eyasmin, On locally $\phi$-symmetric $(LCS)_n$-manifolds, Int. J. Pure Appl. Math. 41 (8), 1161-1170, 2007.
  12. A.A. Shaikh, T. Basu and S. Eyasmin, On the existence of ϕ-recurrent $(LCS)_n$- manifolds, Extracta Mathematica 23 (1), 71-83, 2008.
  13. A.A. Shaikh and U.C. De, On 3-dimensional LP-Sasakian manifolds, Soochow J. Math. 26 (4), 359-368, 2000.
  14. A.A. Shaikh and S.K. Hui, On locally $\phi$-symmetric $\beta$-Kenmotsu manifolds, Extracta Mathematica 24 (3), 301-316, 2010.
  15. A.A. Shaikh and S.K. Hui, On extended $\phi$-recurrent $\beta$-Kenmotsu manifolds, Publi. de l’ Inst. Math., Nouvelle serie, 89 (103), 77-88, 2011.
  16. A.A. Shaikh and H. Kundu, On equivalency of various geometric structures, J. Geom. 105, 139-165, 2014.
  17. Z.I. Szabó, Structure theorems on Riemannian spaces satisfying $R(X,Y)\cdot R=0$, I, The local version, J. Diff. Geom. 17, 531-582, 1982.
  18. Z.I. Szabó, Structure theorems on Riemannian spaces satisfying $R(X,Y)\cdot R=0$, II, Global version, Geom. Dedicata 19, 65-108, 1983.
  19. Z.I. Szabó, Classification and construction of complete hypersurfaces satisfying $R(X,Y)\cdot R=0$, Acta. Sci. Math. 47, 321-348, 1984.
  20. T. Takahashi, Sasakian $\phi$-symmetric spaces, Tohoku Math. J. 29, 91-113, 1977.
  21. S. Tanno, Isometric immersions of Sasakian manifold in spheres, Kodai Math. Sem. Rep. 21, 448-458, 1969.
  22. K. Yano and M. Kon, Structures on manifolds, World Scientific Publ., Singapore, 1984.
  23. H. Weyl, Reine infinitesimal geometrie, Math. Zeitschrift 2, 384-411, 1918.