Research Article
Year 2021,
Volume: 3 Issue: 1, 16 - 22, 30.08.2021
Abstract
References
- Arslan, K., Murathan C. & Özgür C. (2000). On contact manifolds satisfying certain curvature conditions. An. Univ. Bucuresti Math., 49(2), 17-26.
- Atçeken, M. (2014). On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor. Bull. Math. Anal. Appl., 6(1), 1-8.
- Atçeken, M. & Uygun P. (2020). Characterizations for totally geodesic submanifolds of (k;m)-paracontact metric manifolds. Korean J. Math., 28(3), 555-571.
- Calvaruso, G. (2011). Homogeneous paracontact metric three-manifolds, Illinois Journal of Mathematics, 55(2), 697-718.
- Cappelletti-Montano, B., Küpeli Erken, I. & Murathan C. (2012). Nullity conditions in paracontact geometry. Differential Geom. Appl., 30(6), 665-693.
- Kaneyuki, S., Williams, F. L. (1985). Almost paracontact and parahodge structures on manifolds. Nagoya Mathematical Journal, 99, 173-187.
- Kowalczyk, D. (2001). On some subclass of semisymmetric manifolds. Soochow J. Math., 27(4), 445-462.
- Mirzoyan, V. A. (1992). Structure theorems on Riemannian Ricci semisymmetric spaces (Russian), Izv. Vyssh. Uchebn. Zaved. Mat., 6, 80-89.
- Szabo, Z. I. (1982). Structure theorems on Riemannian spaces satisfying R(X;Y):R = 0;. I. The local version. Journal of Differential Geometry, 17(4), 531-582.
- Takahashi, T. (1977). Sasakian $\varphi$-symmetric spaces. Tohoku Math. J., 29(1), 91-113.
- Kon, M., & Yano, K. (1985). Structures on manifolds (Vol. 3). World scientific.
- Uygun P. & Atçeken M. (2021). On $(k,\mu )$-paracontact metric spaces satisfying some conditions on the $W_{0}^{\star }-$curvature tensor. NTMSCI, 9(2), 26-37.
- Yıldırım, Ü ., Atçeken, M. & Dirik, S. (2019). A normal paracontact metric manifold satisfying some conditions on the $M$-projective curvature tensor. Konuralp Journal of Mathematics, 7(1), 217-221.
- Yıldırım, Ü ., Atçeken, M. & Dirik, S. (2019). Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(1), 997-1006.
- Zamkovoy S. (2009). Canonical connections on paracontact manifolds. Ann. Global Anal. Geom., 36(1), 37-60.
- Zamkovoy S. & Tzanov V. (2011). Non-existence of flat paracontact metric structures in dimension greater than or equal to five. Annuaire Univ. Sofia Fac. Math. Inform., 100, 27-34.
Year 2021,
Volume: 3 Issue: 1, 16 - 22, 30.08.2021
Abstract
In the present paper, we have studied the curvature tensors of (k,μμ)-paracontact metric manifold satisfying the conditions ˜Z(X,Y)⋅R=0Z~(X,Y)⋅R=0, ˜ZZ~, \ R(X,Y)⋅˜Z=0R(X,Y)⋅Z~=0 and $R(X,Y)\cdot R=0$. According the cases, we have classified (k,μk,μ)-paracontact metric manifolds.
Keywords
($k,\mu$)-paracontact manifold $\eta$-Einstein manifold concircular curvature tensor Riemannian curvature tensor
References
- Arslan, K., Murathan C. & Özgür C. (2000). On contact manifolds satisfying certain curvature conditions. An. Univ. Bucuresti Math., 49(2), 17-26.
- Atçeken, M. (2014). On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor. Bull. Math. Anal. Appl., 6(1), 1-8.
- Atçeken, M. & Uygun P. (2020). Characterizations for totally geodesic submanifolds of (k;m)-paracontact metric manifolds. Korean J. Math., 28(3), 555-571.
- Calvaruso, G. (2011). Homogeneous paracontact metric three-manifolds, Illinois Journal of Mathematics, 55(2), 697-718.
- Cappelletti-Montano, B., Küpeli Erken, I. & Murathan C. (2012). Nullity conditions in paracontact geometry. Differential Geom. Appl., 30(6), 665-693.
- Kaneyuki, S., Williams, F. L. (1985). Almost paracontact and parahodge structures on manifolds. Nagoya Mathematical Journal, 99, 173-187.
- Kowalczyk, D. (2001). On some subclass of semisymmetric manifolds. Soochow J. Math., 27(4), 445-462.
- Mirzoyan, V. A. (1992). Structure theorems on Riemannian Ricci semisymmetric spaces (Russian), Izv. Vyssh. Uchebn. Zaved. Mat., 6, 80-89.
- Szabo, Z. I. (1982). Structure theorems on Riemannian spaces satisfying R(X;Y):R = 0;. I. The local version. Journal of Differential Geometry, 17(4), 531-582.
- Takahashi, T. (1977). Sasakian $\varphi$-symmetric spaces. Tohoku Math. J., 29(1), 91-113.
- Kon, M., & Yano, K. (1985). Structures on manifolds (Vol. 3). World scientific.
- Uygun P. & Atçeken M. (2021). On $(k,\mu )$-paracontact metric spaces satisfying some conditions on the $W_{0}^{\star }-$curvature tensor. NTMSCI, 9(2), 26-37.
- Yıldırım, Ü ., Atçeken, M. & Dirik, S. (2019). A normal paracontact metric manifold satisfying some conditions on the $M$-projective curvature tensor. Konuralp Journal of Mathematics, 7(1), 217-221.
- Yıldırım, Ü ., Atçeken, M. & Dirik, S. (2019). Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(1), 997-1006.
- Zamkovoy S. (2009). Canonical connections on paracontact manifolds. Ann. Global Anal. Geom., 36(1), 37-60.
- Zamkovoy S. & Tzanov V. (2011). Non-existence of flat paracontact metric structures in dimension greater than or equal to five. Annuaire Univ. Sofia Fac. Math. Inform., 100, 27-34.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | August 30, 2021 |
| Published in Issue | Year 2021 Volume: 3 Issue: 1 |
