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Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces

Yıl 2022, Cilt: 5 Sayı: 4, 161 - 169, 30.12.2022

Pakize Uygun Süleyman Dirik Mehmet Atçeken Tuğba Mert

https://doi.org/10.33434/cams.1171815

Öz

The aim of this paper is to classify $(k,\mu)$-paracontact metric spaces satisfying certain curvature conditions. We present the curvature tensors of (k,$\mu $)-Paracontact manifold satisfying the conditions $R\cdot W_{6}=0$, $ R\cdot W_{7}=0$, $R\cdot W_{8}=0$ and $R\cdot W_{9}=0$. According these cases, $(k,\mu)$-Paracontact manifolds have been characterized. Also, several results are obtained.

Anahtar Kelimeler

(k.mu)-paracontact manifold eta-Einstein manifold Riemannian curvature tensor

Kaynakça

  • [1] D. V. Aleekseevski, C. Medori, A. Tomassini, Maximally homogeneous para-CR manifolds, Ann. Glob. Anal. Geom., 30 (2006), 1-27.
  • [2] M. Atc¸eken, P. Uygun, Characterizations for totally geodesic submanifolds of (k;m)-paracontact metric manifolds, Korcan J. Math., 28(2020), 555-571.
  • [3] G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55 (2011), 697-718.
  • [4] B. Cappelletti-Montano, I. K¨upeli Erken, C. Murathan, Nullity conditions in paracontact geometry, Differential Geom. Appl., 30 (2012), 665-693.
  • [5] S. Kaneyuki, F. L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • [6] B. O. Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [7] G. P. Pokhariyal, Relativistic significance of curvature tensors, Internat. J. Math. Math. Sci., 5 (1) (1982), 133-139.
  • [8] M. M. Tripathi, P. Gupta, T􀀀curvature tensor on a semi-Riemannian manifold, 4 (1) (2011), 117-129.
  • [9] P. Uygun, M. Atc¸eken, On (k;m)-paracontact metricspaces satisfying some conditions on theW? 0 􀀀 curvature tensor, New Trend Math. Sci., 9 (2) (2021), 26-37.
  • [10] P. Uygun, S. Dirik, M. Atc¸eken, T. Mert, The geometry of invariant submanifolds of a (k;m)-paracontact metric manifold, Int. J. Eng. Technol., 84 (1) (2022), 355-363.
  • [11] P. Uygun, S. Dirik, M. Atc¸eken, T. Mert, Some characterizations invariant submanifolds of a (k;m)-paracontact space, Journal of Engineering and Research and Applied Science, 11 (1), (2022), 1967-1972.
  • [12] V. Venkatesha, S. Basavarajappa, Invariant submanifolds of LP-Sasakian manifolds, Khayyam J. Math., 6 (1) (2020), 16-26.
  • [13] V. Venkatesha, S. Basavarajappa,W2-Curvature tensor on generalized sasakian space forms, Cubo A Mathematical Journal, 20(1) (2018), 17-29.
  • [14] K. Yano, M. Kon, Structures Manifolds, Singapore, World Scientific, 1984.
  • [15] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36 (2009), 37-60.
  • [16] S. Zamkovoy, V. Tzanov, 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.

Yıl 2022, Cilt: 5 Sayı: 4, 161 - 169, 30.12.2022

Pakize Uygun Süleyman Dirik Mehmet Atçeken Tuğba Mert

https://doi.org/10.33434/cams.1171815

Öz

Kaynakça

  • [1] D. V. Aleekseevski, C. Medori, A. Tomassini, Maximally homogeneous para-CR manifolds, Ann. Glob. Anal. Geom., 30 (2006), 1-27.
  • [2] M. Atc¸eken, P. Uygun, Characterizations for totally geodesic submanifolds of (k;m)-paracontact metric manifolds, Korcan J. Math., 28(2020), 555-571.
  • [3] G. Calvaruso, Homogeneous paracontact metric three-manifolds, Illinois J. Math., 55 (2011), 697-718.
  • [4] B. Cappelletti-Montano, I. K¨upeli Erken, C. Murathan, Nullity conditions in paracontact geometry, Differential Geom. Appl., 30 (2012), 665-693.
  • [5] S. Kaneyuki, F. L. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
  • [6] B. O. Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [7] G. P. Pokhariyal, Relativistic significance of curvature tensors, Internat. J. Math. Math. Sci., 5 (1) (1982), 133-139.
  • [8] M. M. Tripathi, P. Gupta, T􀀀curvature tensor on a semi-Riemannian manifold, 4 (1) (2011), 117-129.
  • [9] P. Uygun, M. Atc¸eken, On (k;m)-paracontact metricspaces satisfying some conditions on theW? 0 􀀀 curvature tensor, New Trend Math. Sci., 9 (2) (2021), 26-37.
  • [10] P. Uygun, S. Dirik, M. Atc¸eken, T. Mert, The geometry of invariant submanifolds of a (k;m)-paracontact metric manifold, Int. J. Eng. Technol., 84 (1) (2022), 355-363.
  • [11] P. Uygun, S. Dirik, M. Atc¸eken, T. Mert, Some characterizations invariant submanifolds of a (k;m)-paracontact space, Journal of Engineering and Research and Applied Science, 11 (1), (2022), 1967-1972.
  • [12] V. Venkatesha, S. Basavarajappa, Invariant submanifolds of LP-Sasakian manifolds, Khayyam J. Math., 6 (1) (2020), 16-26.
  • [13] V. Venkatesha, S. Basavarajappa,W2-Curvature tensor on generalized sasakian space forms, Cubo A Mathematical Journal, 20(1) (2018), 17-29.
  • [14] K. Yano, M. Kon, Structures Manifolds, Singapore, World Scientific, 1984.
  • [15] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geom., 36 (2009), 37-60.
  • [16] S. Zamkovoy, V. Tzanov, 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Pakize Uygun

Süleyman Dirik 0000-0001-9093-1607

Mehmet Atçeken 0000-0002-1242-4359

Tuğba Mert 0000-0001-8258-8298

Yayımlanma Tarihi 30 Aralık 2022
Gönderilme Tarihi 6 Eylül 2022
Kabul Tarihi 15 Kasım 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 4

Kaynak Göster

APA Uygun, P., Dirik, S., Atçeken, M., Mert, T. (2022). Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces. Communications in Advanced Mathematical Sciences, 5(4), 161-169. https://doi.org/10.33434/cams.1171815
AMA Uygun P, Dirik S, Atçeken M, Mert T. Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces. Communications in Advanced Mathematical Sciences. Aralık 2022;5(4):161-169. doi:10.33434/cams.1171815
Chicago Uygun, Pakize, Süleyman Dirik, Mehmet Atçeken, ve Tuğba Mert. “Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces”. Communications in Advanced Mathematical Sciences 5, sy. 4 (Aralık 2022): 161-69. https://doi.org/10.33434/cams.1171815.
EndNote Uygun P, Dirik S, Atçeken M, Mert T (01 Aralık 2022) Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces. Communications in Advanced Mathematical Sciences 5 4 161–169.
IEEE P. Uygun, S. Dirik, M. Atçeken, ve T. Mert, “Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces”, Communications in Advanced Mathematical Sciences, c. 5, sy. 4, ss. 161–169, 2022, doi: 10.33434/cams.1171815.
ISNAD Uygun, Pakize vd. “Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces”. Communications in Advanced Mathematical Sciences 5/4 (Aralık 2022), 161-169. https://doi.org/10.33434/cams.1171815.
JAMA Uygun P, Dirik S, Atçeken M, Mert T. Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces. Communications in Advanced Mathematical Sciences. 2022;5:161–169.
MLA Uygun, Pakize vd. “Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces”. Communications in Advanced Mathematical Sciences, c. 5, sy. 4, 2022, ss. 161-9, doi:10.33434/cams.1171815.
Vancouver Uygun P, Dirik S, Atçeken M, Mert T. Certain Curvature Conditions on $(k,\mu )$-Paracontact Metric Spaces. Communications in Advanced Mathematical Sciences. 2022;5(4):161-9.
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