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On Almost C(α)-Manifold Satisfying Certain Curvature Conditions

Year 2024, Volume: 45 Issue: 1, 135 - 146, 28.03.2024

Tuğba Mert , Mehmet Atçeken , Pakize Uygun

https://doi.org/10.17776/csj.1312302

Abstract

This research article is about the geometry of the almost C(α)- manifold. Some important properties of the almost C(α)- manifold with respect to the W_3- curvature tensor, such as W_3-flat and W_3- semi-symmetry, are investigated. The relationship of W_3- curvature tensor with Riemann, Ricci, projective, concircular and quasi-conformal curvature tensor is discussed on the almost C(α)- manifold and many important results are obtained. In addition, W_3- pseudo symmetry and W_3- Ricci pseudo symmetry are investigated for the almost C(α)- manifold. The results obtained are interesting and give an idea about the geometry of the almost C(α)- manifold.

Keywords

C(α)-Manifold W_3-Curvature Tensor Pseudo-symmetric manifold

References

  • [1] Kaneyuki, S., Williams, F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985) 173-187.
  • [2] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36 (2009) 37-60.
  • [3] Atçeken, M., Uygun, P., Characterizations for totally geodesic submanifolds of (k,μ)-paracontact metric manifolds, Korean J. Math., 28 (2020) 555-571.
  • [4] Atçeken, M., Dirik, S., On the geometry of pseudo-slant submanifolds of a Kenmotsu manifold, Gulf Journal of Mathematics, 2 (2014) 51-66.
  • [5] Laha, B., Das, B., Bhattacharyya, A., Submanifolds of some indefinite contact and paracontact metric manifolds, Gulf Journal of Mathematics, 1 (2013) 180-188.
  • [6] Yıldırım, Ü., Atçeken, M., Dirik,S., Generalized B-curvature tensor of normal paracntact metric manifold, Hagia Sophia Journal of Geometry, 1 (2009) 1-7.
  • [7] Yıldırım, Ü., Atçeken, M., Dirik, S., Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1, Math. Stat., 68 (2019) 997-1006.
  • [8] Capelletti-Montano, B., Küpeli Erken, I., Murathan, C., Nullity conditions in paracontact geometry, Differential Geom. Appl., 30 (2012) 665-693.
  • [9] Kowalczyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math., 27 (2001) 445-461.
  • [10] Szabo, Z.I., Structure theorems on riemannian spaces satisfying R(ϖ_1,ϖ_2 )R=0, I: The local Version, J. Differential Geom., 17 (1982) 531-582.
  • [11] Tripathi, M., Gupta, P., T-Curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Studies, 4 (1) (2011) 117-129.
  • [12] 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 (2010) 1-14.
  • [13] De, U.C., Sarkar, A., On the Projective curvature tensor of generalized Sasakian space forms, Questiones Mathematicae, 33 (2010) 245-252.
  • [14] Atçeken, M., On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Mathematical Analysis and Applications, 6 (2014) 1-8.
  • [15] Özgür, C., De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17 (2006) 221-228.
  • [16] Arslan, K., Murathan, C., Özgür, C., On contact manifolds satisfying certain curvature conditions, An. Univ. Bucuresti Math., 49 (2000) 17-26.
  • [17] Pokhariyal, G.P., Mishra, R.S., Curvature tensors and their relativistic significance II, Yokohama Math. J., 19 (1971) 97-103.
  • [18] Ojha, R., M-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math., 17 (1986) 481-484.
  • [19] Uygun, P., Atçeken, M., On (κ,μ)-paracontact metric spaces satisfying some conditions on the W_0-curvature tensor, New Trends in Mathematical Sciences, 9 (2) 2021 26-37.
  • [20]Janssens, D., Vanhecke, L., Almost contact structure and curvature tensors, Kodai Math. J., 4 (1981) 1-27.
  • [21] Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad., Tokyo, 16 (1940) 195-200.
  • [22] Yano, K., Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2 (1968) 161-184.
  • [23]Mert, T., On a Classification of Almost C(α)-Manifolds, Journal of Mathematics, (2022).
  • [24]Mert, T., Characterization of Some Special Curvature Tensor on Almost C(α)-Manifold, Asian Journal of Mathematics and Computer Research, 29 (1) (2022) 27-41.
  • [25]Mert, T., Atçeken, M., Almost C(α)-Manifold on W_0^*-Curvature Tensor, Applied Mathematical Sciences, 15 (15) (2021) 693-703.

Year 2024, Volume: 45 Issue: 1, 135 - 146, 28.03.2024

Tuğba Mert , Mehmet Atçeken , Pakize Uygun

https://doi.org/10.17776/csj.1312302

Abstract

References

  • [1] Kaneyuki, S., Williams, F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985) 173-187.
  • [2] Zamkovoy, S., Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36 (2009) 37-60.
  • [3] Atçeken, M., Uygun, P., Characterizations for totally geodesic submanifolds of (k,μ)-paracontact metric manifolds, Korean J. Math., 28 (2020) 555-571.
  • [4] Atçeken, M., Dirik, S., On the geometry of pseudo-slant submanifolds of a Kenmotsu manifold, Gulf Journal of Mathematics, 2 (2014) 51-66.
  • [5] Laha, B., Das, B., Bhattacharyya, A., Submanifolds of some indefinite contact and paracontact metric manifolds, Gulf Journal of Mathematics, 1 (2013) 180-188.
  • [6] Yıldırım, Ü., Atçeken, M., Dirik,S., Generalized B-curvature tensor of normal paracntact metric manifold, Hagia Sophia Journal of Geometry, 1 (2009) 1-7.
  • [7] Yıldırım, Ü., Atçeken, M., Dirik, S., Pseudo projective curvature tensor satisfying some properties on a normal paracontact metric manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1, Math. Stat., 68 (2019) 997-1006.
  • [8] Capelletti-Montano, B., Küpeli Erken, I., Murathan, C., Nullity conditions in paracontact geometry, Differential Geom. Appl., 30 (2012) 665-693.
  • [9] Kowalczyk, D., On some subclass of semisymmetric manifolds, Soochow J. Math., 27 (2001) 445-461.
  • [10] Szabo, Z.I., Structure theorems on riemannian spaces satisfying R(ϖ_1,ϖ_2 )R=0, I: The local Version, J. Differential Geom., 17 (1982) 531-582.
  • [11] Tripathi, M., Gupta, P., T-Curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Studies, 4 (1) (2011) 117-129.
  • [12] 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 (2010) 1-14.
  • [13] De, U.C., Sarkar, A., On the Projective curvature tensor of generalized Sasakian space forms, Questiones Mathematicae, 33 (2010) 245-252.
  • [14] Atçeken, M., On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Mathematical Analysis and Applications, 6 (2014) 1-8.
  • [15] Özgür, C., De, U.C., On the quasi-conformal curvature tensor of a Kenmotsu manifold, Mathematica Pannonica, 17 (2006) 221-228.
  • [16] Arslan, K., Murathan, C., Özgür, C., On contact manifolds satisfying certain curvature conditions, An. Univ. Bucuresti Math., 49 (2000) 17-26.
  • [17] Pokhariyal, G.P., Mishra, R.S., Curvature tensors and their relativistic significance II, Yokohama Math. J., 19 (1971) 97-103.
  • [18] Ojha, R., M-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math., 17 (1986) 481-484.
  • [19] Uygun, P., Atçeken, M., On (κ,μ)-paracontact metric spaces satisfying some conditions on the W_0-curvature tensor, New Trends in Mathematical Sciences, 9 (2) 2021 26-37.
  • [20]Janssens, D., Vanhecke, L., Almost contact structure and curvature tensors, Kodai Math. J., 4 (1981) 1-27.
  • [21] Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad., Tokyo, 16 (1940) 195-200.
  • [22] Yano, K., Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2 (1968) 161-184.
  • [23]Mert, T., On a Classification of Almost C(α)-Manifolds, Journal of Mathematics, (2022).
  • [24]Mert, T., Characterization of Some Special Curvature Tensor on Almost C(α)-Manifold, Asian Journal of Mathematics and Computer Research, 29 (1) (2022) 27-41.
  • [25]Mert, T., Atçeken, M., Almost C(α)-Manifold on W_0^*-Curvature Tensor, Applied Mathematical Sciences, 15 (15) (2021) 693-703.
There are 25 citations in total.

Details

Primary Language English
Subjects Atomic, Molecular and Optical Physics (Other)
Journal Section Natural Sciences
Authors

Tuğba Mert 0000-0001-8258-8298

Mehmet Atçeken 0000-0002-1242-4359

Pakize Uygun 0000-0001-8226-4269

Publication Date March 28, 2024
Submission Date June 9, 2023
Acceptance Date December 21, 2023
Published in Issue Year 2024Volume: 45 Issue: 1

Cite

APA Mert, T., Atçeken, M., & Uygun, P. (2024). On Almost C(α)-Manifold Satisfying Certain Curvature Conditions. Cumhuriyet Science Journal, 45(1), 135-146. https://doi.org/10.17776/csj.1312302
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