Research Article
BibTex RIS Cite

Year 2023, Volume: 15 Issue: 1, 171 - 179, 30.06.2023

Pakize Uygun Mehmet Atçeken

https://doi.org/10.47000/tjmcs.1153650

Abstract

References

  • Arslan, K., Murathan, C., Özgür, C., On contact manifolds satisfying certain curvature conditions, an. Univ. Bucuresti Math. 49(2)(2000), 17-26.
  • 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.
  • Atçeken, M., Uygun, P., Characterizations for totally geodesic submanifolds of $(k,\mu )$-paracontact metric manifolds, Korean J. Math. 28(2020), 555-571.
  • Ayar, G., Chaubey, S.K., M-projective curvature tensor over cosymplectic manifolds, Differential Geometry - Dynamical Systems, 21(2019), 23-33.
  • Calvaruso, G., Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2011), 697-718.
  • Cappelletti-Montano, B., Küpeli Erken, I., Murathan, C., Nullity conditions in paracontact geometry, Differential Geom. Appl., 30(2012), 665-693.
  • De, K., De, U.C., Conharmonic curvature tensor on Kenmotsu manifolds, Bulletin of the Transilvanya Univ., of Brasov, 6(55)(1)(2013).
  • De, U.C., Sarkar, A., On the Projective curvature tensor of Generalized Sasakians-space forms, Questiones Mathematicae, 33(2010), 245-252.
  • Kaneyuki, S., Williams, F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99(1985), 173-187.
  • Kowalezyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math., 27(2001), 445-461.
  • 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.
  • Mert, T., Atçeken, M., Almost $C(a)$-manifold on $W_{0}^{\star }-$curvature tensor, Applied Mathematical Sciences, 15(15)(2021), 693-703.
  • 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.
  • Mirzoyan, V.A., Structure theorems on Riemannian Ricci semisymmetric spaces (Russian), Izv. Vyssh. Uchebn. Zaved. Mat., 6(1992), 80-89.
  • Murathan, C., Erken, I.K., The harmonicity of the Reeb vector dield on paracontact metric 3-manifolds, arXiv:1305.1511v3 [math.DG], 27(2013).
  • Özgür, C., De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17(2)(2006), 221-228.
  • 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.
  • Takahashi, T., Sasakian $\phi -$symmetric spaces, Tohoku Math. J., 29(1977), 91-113.
  • Yano, K., Kon, M., Structures Manifolds, Singapore, World Scientific, 1984.
  • Yano, K., Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom. 2(1968), 161-184.
  • Yıldız, A., De, U.C., Murathan, C., Arslan, K., On the weyl projective curvature tensor of an N(k)-contact metric manifold, Mathematica Pannonica, 21(1)(2010),1-14.
  • Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(2009), 37-60.
  • Zamkovoy, S., Tzanov, V., Non-existence of flat paracontact metric structures in dimension greater than or equal to five, Annuaire Univ. Sofia Fac. Math. Inform., 100(2011), 27-34.
  • Zhen, G., On conformal symmetric K-contact manifolds, Chinese Quart. J. of Math., 7(1992), 5-10.

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

Year 2023, Volume: 15 Issue: 1, 171 - 179, 30.06.2023

Pakize Uygun Mehmet Atçeken

https://doi.org/10.47000/tjmcs.1153650

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.

Keywords

$(k,\mu)$-Paracontact manifold Einstein manifold Weyl projective curvature tensor conformal curvature tensor concircular curvature tensor

References

  • Arslan, K., Murathan, C., Özgür, C., On contact manifolds satisfying certain curvature conditions, an. Univ. Bucuresti Math. 49(2)(2000), 17-26.
  • 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.
  • Atçeken, M., Uygun, P., Characterizations for totally geodesic submanifolds of $(k,\mu )$-paracontact metric manifolds, Korean J. Math. 28(2020), 555-571.
  • Ayar, G., Chaubey, S.K., M-projective curvature tensor over cosymplectic manifolds, Differential Geometry - Dynamical Systems, 21(2019), 23-33.
  • Calvaruso, G., Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55(2011), 697-718.
  • Cappelletti-Montano, B., Küpeli Erken, I., Murathan, C., Nullity conditions in paracontact geometry, Differential Geom. Appl., 30(2012), 665-693.
  • De, K., De, U.C., Conharmonic curvature tensor on Kenmotsu manifolds, Bulletin of the Transilvanya Univ., of Brasov, 6(55)(1)(2013).
  • De, U.C., Sarkar, A., On the Projective curvature tensor of Generalized Sasakians-space forms, Questiones Mathematicae, 33(2010), 245-252.
  • Kaneyuki, S., Williams, F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99(1985), 173-187.
  • Kowalezyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math., 27(2001), 445-461.
  • 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.
  • Mert, T., Atçeken, M., Almost $C(a)$-manifold on $W_{0}^{\star }-$curvature tensor, Applied Mathematical Sciences, 15(15)(2021), 693-703.
  • 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.
  • Mirzoyan, V.A., Structure theorems on Riemannian Ricci semisymmetric spaces (Russian), Izv. Vyssh. Uchebn. Zaved. Mat., 6(1992), 80-89.
  • Murathan, C., Erken, I.K., The harmonicity of the Reeb vector dield on paracontact metric 3-manifolds, arXiv:1305.1511v3 [math.DG], 27(2013).
  • Özgür, C., De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17(2)(2006), 221-228.
  • 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.
  • Takahashi, T., Sasakian $\phi -$symmetric spaces, Tohoku Math. J., 29(1977), 91-113.
  • Yano, K., Kon, M., Structures Manifolds, Singapore, World Scientific, 1984.
  • Yano, K., Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom. 2(1968), 161-184.
  • Yıldız, A., De, U.C., Murathan, C., Arslan, K., On the weyl projective curvature tensor of an N(k)-contact metric manifold, Mathematica Pannonica, 21(1)(2010),1-14.
  • Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36(2009), 37-60.
  • Zamkovoy, S., Tzanov, V., Non-existence of flat paracontact metric structures in dimension greater than or equal to five, Annuaire Univ. Sofia Fac. Math. Inform., 100(2011), 27-34.
  • Zhen, G., On conformal symmetric K-contact manifolds, Chinese Quart. J. of Math., 7(1992), 5-10.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Pakize Uygun 0000-0001-8226-4269

Mehmet Atçeken 0000-0002-1242-4359

Publication Date June 30, 2023
Published in Issue Year 2023 Volume: 15 Issue: 1

Cite

APA Uygun, P., & Atçeken, M. (2023). On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. Turkish Journal of Mathematics and Computer Science, 15(1), 171-179. https://doi.org/10.47000/tjmcs.1153650
AMA Uygun P, Atçeken M. On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. TJMCS. June 2023;15(1):171-179. doi:10.47000/tjmcs.1153650
Chicago Uygun, Pakize, and Mehmet Atçeken. “On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions”. Turkish Journal of Mathematics and Computer Science 15, no. 1 (June 2023): 171-79. https://doi.org/10.47000/tjmcs.1153650.
EndNote Uygun P, Atçeken M (June 1, 2023) On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. Turkish Journal of Mathematics and Computer Science 15 1 171–179.
IEEE P. Uygun and M. Atçeken, “On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions”, TJMCS, vol. 15, no. 1, pp. 171–179, 2023, doi: 10.47000/tjmcs.1153650.
ISNAD Uygun, Pakize - Atçeken, Mehmet. “On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions”. Turkish Journal of Mathematics and Computer Science 15/1 (June 2023), 171-179. https://doi.org/10.47000/tjmcs.1153650.
JAMA Uygun P, Atçeken M. On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. TJMCS. 2023;15:171–179.
MLA Uygun, Pakize and Mehmet Atçeken. “On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 1, 2023, pp. 171-9, doi:10.47000/tjmcs.1153650.
Vancouver Uygun P, Atçeken M. On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions. TJMCS. 2023;15(1):171-9.