SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2023 / Cilt: 15 Sayı: 1

On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions

Pakize UYGUN
Mehmet ATÇEKEN
Pages
171–179
Publication Date
2023-06-30
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we studied the curvature tensors of (k,$\mu$) satisfying the conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, $\widetilde{Z}(\xi ,\alpha _{3})\cdot S=0$, $R(\xi ,\alpha _{3})\cdot P=0$, $R(\xi ,\alpha _{3})\cdot S=0$ and $P\cdot C=0$.
📊
Key Findings & Data:Besides this, we classify $(k,\mu)$-paracontact manifolds.
💡
Conclusion & Impact:Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$(k · \mu)$-Paracontact manifold · Einstein manifold

Abstract

In this work, we studied the curvature tensors of (k,$\mu$) satisfying the conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, $\widetilde{Z}(\xi ,\alpha _{3})\cdot S=0$, $R(\xi ,\alpha _{3})\cdot P=0$, $R(\xi ,\alpha _{3})\cdot S=0$ and $P\cdot C=0$. Besides this, we classify $(k,\mu)$-paracontact manifolds. Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.

🔖

Cite This Article

UYGUN, P., ATÇEKEN, M. (2023). On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. Turkish Journal of Mathematics and Computer Science, Cilt: 15 Sayı: 1, 171–179. https://ajindex.com/articles/950950

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Arslan, K., Murathan, C., Özgür, C., On contact manifolds satisfying certain curvature conditions, an. Univ. Bucuresti Math. 49(2)(2000), 17-26.
  2. Atçeken, M., On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Mathematical Analysis and Applications, 6(1)(2014), 1-8.
  3. Atçeken, M., Uygun, P., Characterizations for totally geodesic submanifolds of $(k,\mu )$-paracontact metric manifolds, Korean J. Math. 28(2020), 555-571.
  4. Ayar, G., Chaubey, S.K., M-projective curvature tensor over cosymplectic manifolds, Differential Geometry - Dynamical Systems, 21(2019), 23-33.
  5. Calvaruso, G., Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2011), 697-718.
  6. Cappelletti-Montano, B., Küpeli Erken, I., Murathan, C., Nullity conditions in paracontact geometry, Differential Geom. Appl., 30(2012), 665-693.
  7. De, K., De, U.C., Conharmonic curvature tensor on Kenmotsu manifolds, Bulletin of the Transilvanya Univ., of Brasov, 6(55)(1)(2013).
  8. De, U.C., Sarkar, A., On the Projective curvature tensor of Generalized Sasakians-space forms, Questiones Mathematicae, 33(2010), 245-252.
  9. Kaneyuki, S., Williams, F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99(1985), 173-187.
  10. Kowalezyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math., 27(2001), 445-461.
  11. Mert, T., Characterization of some special curvature tensor on Almost $C(a)$-manifold, Asian Journal of Math. and Computer Research, 29(1)(2022), 27-41.
  12. Mert, T., Atçeken, M., Almost $C(a)$-manifold on $W_{0}^{\star }-$curvature tensor, Applied Mathematical Sciences, 15(15)(2021), 693-703.
  13. Mert, T., Atçeken, M., Some important properties of almost Kenmotsu $\ (k,\mu,\nu )-$space on the concircular curvature tensor, Fundamental Journal of Mathematics and Applications, 6(1)(2023), 51-60.
  14. Mirzoyan, V.A., Structure theorems on Riemannian Ricci semisymmetric spaces (Russian), Izv. Vyssh. Uchebn. Zaved. Mat., 6(1992), 80-89.
  15. Murathan, C., Erken, I.K., The harmonicity of the Reeb vector dield on paracontact metric 3-manifolds, arXiv:1305.1511v3 [math.DG], 27(2013).
  16. Özgür, C., De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17(2)(2006), 221-228.
  17. Szabo, Z.I., Structure theorems on Riemannian sp-aces satisfing $R(\alpha _{4},\alpha _{5}).R=0,$ I: The local version, J. Differential Geom., 17(4)(1982), 531-582.
  18. Takahashi, T., Sasakian $\phi -$symmetric spaces, Tohoku Math. J.,