Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 16 Issue: 1

On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection

Shivani Sundriyal(Kumaun University, Nainital)0000-0001-6195-2572
Sayfa
—
Yayın Tarihi
2023-04-30
🏛️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)

Also, we studied projective curvature tensor, concircular curvature tensor, and Nijenhuis tensor for the Para-Sasakian manifold with respect to the Schouten-van Kampen connection.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In the present paper, we have studied the curvature properties of the Schouten-van Kampen connection on the n-dimensional Para Sasakian manifold and obtained some new results.
📊
Temel Bulgular & Veri:In the present paper, we have studied the curvature properties of the Schouten-van Kampen connection on the n-dimensional Para Sasakian manifold and obtained some new results.
💡
Sonuç & Katkı:Also, we studied projective curvature tensor, concircular curvature tensor, and Nijenhuis tensor for the Para-Sasakian manifold with respect to the Schouten-van Kampen connection.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Para-Sasakian manifold · Schouten-van Kampen connection · Concircular curvature tensor

Abstract

In the present paper, we have studied the curvature properties of the Schouten-van Kampen connection on the n-dimensional Para Sasakian manifold and obtained some new results. Also, we studied projective curvature tensor, concircular curvature tensor, and Nijenhuis tensor for the Para-Sasakian manifold with respect to the Schouten-van Kampen connection.

🔖

Bu Makaleye Atıf Yap

Sundriyal, S., Upreti, J. (2023). On Para-Sasakian Manifold with Respect to the Schouten-van Kampen Connection. International Electronic Journal of Geometry, Volume: 16 Issue: 1. https://doi.org/10.36890/iejg.1200729

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (30)

  1. Adati, T., Miiyazawa.: On P-Sasakian manifolds satisfying certain conditions. Tensor(N.S) 33, 173-178 (1979).
  2. Bejancu, A., Faran, H.: Foliations and Geometric Structures. Dordrecht, Netherlands, (2006).
  3. Bejancu, A.: Schouten-van Kampen and Vranceanu connections on Foliated manifolds Anal. Univ.(Al.I.Cuza’Iasi Mat.) 52, 37-60 (2006).
  4. Ghosh, G.: On Schouten-van Kampen connection on Sasakian manifolds Bo-letim da Sociedade Paranaense de Matematica. 36, 171-182 (2018).
  5. Ianus, S.: Some almost product structures on manifolds with the linear connection Kodai Mathematical Seminar Reports. 23, 305-310 (1971).
  6. Kuhnel, W.: Conformal transformations between Einstein spaces. Aspects Math. E12, Friedr. Vieweg, Braunschweing, 1988.
  7. Mandal, K., De, U.C.: Quarter-symmetric metric connection in a P-Sasakian manifold, Annals of West University of Timisoara-Mathematics and Computer Science. 53 (1), 137-150 (2015).
  8. Matsumoto, K., Ianus, S., Mihai, I.: On P-Sasakian manifolds which admit certain tensor-fields Publicationes Mathematicae-Debrecen. 33, 199-205 (1986).
  9. Mondal, A.: On f-Kenmotsu manifolds admitting Schouten-Van Kampen connection The Korean Journal of Mathematics, Gorakhpur. 29 (2), 333-344 (2021).
  10. Nagaraja, H. G., Kumar, D.L.K.: Kenmotsu manifolds admitting Schouten-van Kampen Connection Facta Universitatis, Series: Mathematics and Informatics. 34, 23-34 (2019).
  11. Olszak, Z.: The Schouten–van Kampen affine connection adapted an almost (para) contact metric structure. Publications de l’Institut Mathematique. 94, 31-42 (2013).
  12. Olszak, Z., Rosca, R.: Normal locally conformal almost cosymplectic manifolds Publicationes Mathematicae Debrecen. 39, 315-323 (1991).
  13. Ozgur, C., On A class of para-Sakakian manifolds Turkish Journal of Mathematics. 29(3), 249-258 (2005).
  14. Perktas, Y.S., Yildiz, A.: On Quasi-Sasakian 3-Manifolds with Respect to the Schouten-van Kampen Connection International Electronic Journal of Geometry. 13 (2), 62-74 (2020).
  15. Perktas, Y.S., Yildiz, A.: On f-Kenmotsu 3-manifolds with respect to the Schouten-van Kampen connection Turkish J. of Math. 45, 387-409 (2021).
  16. Sasaki, S., Hatakeyama, Y.: On differentiable manifolds with certain structures which are closely related to almost contact structures II Tohoku Mathematical Journal, 13, 281-294 (1961).
  17. Sato, I.: On a structure similar to the almost contact structure Tensor(N.S). 30, 219-224 (1976).
  18. Sato, I., Matsumoto, K.: On P-Sahakian manifolds satisfying certain conditions Tensor(N.S). 33, 173-178 (1979).
  19. Schouten, J., van Kampen, E.: Zur Einbettungs-und Krummungsthorie nichtholonomer Gebilde Mathematische Annalen. 103, 752-783 (1930).
  20. Shukla, S. S., Shukla, M. K.: On ϕ-symmetric Para-Sasakian manifolds Int. J. Math. Analysis, 16 (4), 761-769 (2010).
  21. Solov’ev, A. F.: On the curvature of the connection induced on a hyperdistribution in a Riemannian space Geometricheskii Sbornik. 19, 12-23 (1978).
  22. Solov’ev, A. F.: The bending of hyperdistributions Geometricheskii Sbornik. 20, 101-112 (1979).
  23. Solov’ev, A. F.: Second fundamental form of a distribution Matematicheskie Zametki. 35, 139-146 (1982).
  24. Solov’ev, A. F.: Curvature of a distribution Matematicheskie Zametki. 35, 111-124 (1984).
  25. Yano, K.: Concircular geometry I. concircular transformations Proc. Inst. Acad. Tokyo. 16, 195-200 (1940).
  26. Yano, K., Bochner, S.: Curvature and Betti numbers. Annals of Math. Studies 32, Princeton university press, 1953.
  27. Yano, K., Kon, M.: Structures on manifolds, Series in Pure Mathematics, 3. World Scientific, 1984.
  28. Yıldız, A.: f-Kenmotsu manifolds with the Schouten–van Kampen connection Publications de l’Institut Mathematique. 102 (116), 93-105 (2017).
  29. Yıldız, A., Turan, M., Acet, B. E.: On Para-Sasakian manifolds Journal of Science and Technology of Dumlupınar University. 24, 27-34 (2011).
  30. Olszak, Z.: The Schouten–van Kampen affine connection adapted an almost (para) contact metric structure. Publications de l’Institut Mathematique. 94, 31-42 (2013).