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On Quasi-Conformal Flat Para-Sasakian Manifolds

Yıl 2020, Cilt: 12 Sayı: 2, 86 - 91, 31.12.2020
https://doi.org/10.47000/tjmcs.765297

Öz

In this paper, we present some new results on invariant submanifolds of a para-Sasakian manifold under the quasi-conformally flatness condition. Firstly, we examine flatness of quasi-conformal curvature tensor on para-Sasakian manifolds. We prove that a quasi-conformally flat para-Sasakian manifold is an $ \eta $-Einstein manifold. Also, we give some results on the sectional curvature of such manifolds. Secondly, we consider the invariant submanifolds of a quasi-conformally flat para-Sasakian manifold. We prove that a totally umbilical submanifold of a para-Sasakian manifold is invariant. In addition, we investigate curvature properties of such submanifolds and we show that a totally umbilical invariant submanifold of a quasi-conformally flat para-Sasakian manifold is an $ \eta $-Einstein manifold. Finally, we work on the sectional curvature properties of an invariant submanifold of a quasi-conformally flat para-Sasakian manifold.

Kaynakça

  • Adati, T., \textit{On conformally recurrent and conformally symmetric P-Sasakian manifolds}, TRU Math., \textbf{13}(1977), 25-32.
  • Aksoy Sar\i, E., \"Unal, \.I, Sar\i, R., \textit{CR submanifolds of para Sasakian manifolds with semi-symmetric non-metric connection}, Proceeding Book of 4. (2019) International Conference on Computational Mathematics and Engineering Sciences Antalya ISBN: 77733.
  • Blair, D. E., Riemannian geometry of contact and symplectic manifolds. Springer Science and Business Media (2010).
  • De, U. C., Pathak, G.,\textit{ On P-Sasakian manifolds satisfying certain conditions}, J. Indian Acad. Math. \textbf{16}(1994), 72-77.
  • De, U. C., Guha, N.,\textit{ On a type of P-Sasakian manifold}, \.Istanbul Univ. Fen Fak. Mat. Der. \textbf{51}(1992), 35-39.
  • De, U. C., \"Ozg\"ur, K., Arslan, C., Murathan, A., Y\i ld\i z, \textit{On a type of para-Sasakian manifold}, Mathematica balcanica, \textbf{22}(2008), 25-36.
  • Kaneyuki, S., Williams, F. L., \textit{Almost paracontact and parahodge structures on manifolds}, Nagoya Mathematical Journal, \textbf{99}(1985), 173-187.
  • \"Ozg\"ur, C., Tripathi, M. M. \textit{On P-Sasakian manifolds satisfying certain conditions on the concircular curvature tensor}, Turk J Math., \textbf{31}(2)(2007), 171-179.
  • Sasaki, S., Almost contact manifolds, Lecture notes. Mathematical institute, Tohoku University, \textbf{19}(1965), 65.
  • Turgut Vanli, A., \"Unal, I., \textit{Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds}, International Journal of Geometric Methods in Modern Physics, \textbf{14}(05)(2017), 1750067.
  • \"Unal, I., \textit{Some Flatness Conditions on Normal Metric Contact Pairs}, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., \textbf{69}(2020), 262-271.
  • Turgut Vanli, A., \"Unal, I., \textit{H-curvature tensors on IK-normal complex contact metric manifolds}, International Journal of Geometric Methods in Modern Physics, \textbf{15}(12) (2018), 185-205.
  • \"Unal, I., Sari, R., Vanli Turgut, A., \textit{Concircular curvature tensor on generalized Kenmotsu manifolds}, G\"um\"u\c{s}hane University Journal of Science and Technology Institute, (2018), 99-105.
  • Yano, K., Kon, M., \textit{Structures on manifolds}, Series in Pure Mathematics, \textbf{3}(1984) World Scientific, https://doi.org/10.1142/0067
  • Yano, K., Sawaski, S., \textit{Riemannian manifolds admitting a conformal transformation group}, J. Diff. Geo. \textbf{2}(1968)
  • Zamkovoy, S., \textit{Canonical connections on paracontact manifolds}, Annals of Global Analysis and Geometry, \textbf{36}(1) (2009), 37-60.
Yıl 2020, Cilt: 12 Sayı: 2, 86 - 91, 31.12.2020
https://doi.org/10.47000/tjmcs.765297

Öz

Kaynakça

  • Adati, T., \textit{On conformally recurrent and conformally symmetric P-Sasakian manifolds}, TRU Math., \textbf{13}(1977), 25-32.
  • Aksoy Sar\i, E., \"Unal, \.I, Sar\i, R., \textit{CR submanifolds of para Sasakian manifolds with semi-symmetric non-metric connection}, Proceeding Book of 4. (2019) International Conference on Computational Mathematics and Engineering Sciences Antalya ISBN: 77733.
  • Blair, D. E., Riemannian geometry of contact and symplectic manifolds. Springer Science and Business Media (2010).
  • De, U. C., Pathak, G.,\textit{ On P-Sasakian manifolds satisfying certain conditions}, J. Indian Acad. Math. \textbf{16}(1994), 72-77.
  • De, U. C., Guha, N.,\textit{ On a type of P-Sasakian manifold}, \.Istanbul Univ. Fen Fak. Mat. Der. \textbf{51}(1992), 35-39.
  • De, U. C., \"Ozg\"ur, K., Arslan, C., Murathan, A., Y\i ld\i z, \textit{On a type of para-Sasakian manifold}, Mathematica balcanica, \textbf{22}(2008), 25-36.
  • Kaneyuki, S., Williams, F. L., \textit{Almost paracontact and parahodge structures on manifolds}, Nagoya Mathematical Journal, \textbf{99}(1985), 173-187.
  • \"Ozg\"ur, C., Tripathi, M. M. \textit{On P-Sasakian manifolds satisfying certain conditions on the concircular curvature tensor}, Turk J Math., \textbf{31}(2)(2007), 171-179.
  • Sasaki, S., Almost contact manifolds, Lecture notes. Mathematical institute, Tohoku University, \textbf{19}(1965), 65.
  • Turgut Vanli, A., \"Unal, I., \textit{Conformal, concircular, quasi-conformal and conharmonic flatness on normal complex contact metric manifolds}, International Journal of Geometric Methods in Modern Physics, \textbf{14}(05)(2017), 1750067.
  • \"Unal, I., \textit{Some Flatness Conditions on Normal Metric Contact Pairs}, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., \textbf{69}(2020), 262-271.
  • Turgut Vanli, A., \"Unal, I., \textit{H-curvature tensors on IK-normal complex contact metric manifolds}, International Journal of Geometric Methods in Modern Physics, \textbf{15}(12) (2018), 185-205.
  • \"Unal, I., Sari, R., Vanli Turgut, A., \textit{Concircular curvature tensor on generalized Kenmotsu manifolds}, G\"um\"u\c{s}hane University Journal of Science and Technology Institute, (2018), 99-105.
  • Yano, K., Kon, M., \textit{Structures on manifolds}, Series in Pure Mathematics, \textbf{3}(1984) World Scientific, https://doi.org/10.1142/0067
  • Yano, K., Sawaski, S., \textit{Riemannian manifolds admitting a conformal transformation group}, J. Diff. Geo. \textbf{2}(1968)
  • Zamkovoy, S., \textit{Canonical connections on paracontact manifolds}, Annals of Global Analysis and Geometry, \textbf{36}(1) (2009), 37-60.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

İnan Ünal 0000-0003-1318-9685

Ramazan Sarı 0000-0002-4618-8243

Yayımlanma Tarihi 31 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 12 Sayı: 2

Kaynak Göster

APA Ünal, İ., & Sarı, R. (2020). On Quasi-Conformal Flat Para-Sasakian Manifolds. Turkish Journal of Mathematics and Computer Science, 12(2), 86-91. https://doi.org/10.47000/tjmcs.765297
AMA Ünal İ, Sarı R. On Quasi-Conformal Flat Para-Sasakian Manifolds. TJMCS. Aralık 2020;12(2):86-91. doi:10.47000/tjmcs.765297
Chicago Ünal, İnan, ve Ramazan Sarı. “On Quasi-Conformal Flat Para-Sasakian Manifolds”. Turkish Journal of Mathematics and Computer Science 12, sy. 2 (Aralık 2020): 86-91. https://doi.org/10.47000/tjmcs.765297.
EndNote Ünal İ, Sarı R (01 Aralık 2020) On Quasi-Conformal Flat Para-Sasakian Manifolds. Turkish Journal of Mathematics and Computer Science 12 2 86–91.
IEEE İ. Ünal ve R. Sarı, “On Quasi-Conformal Flat Para-Sasakian Manifolds”, TJMCS, c. 12, sy. 2, ss. 86–91, 2020, doi: 10.47000/tjmcs.765297.
ISNAD Ünal, İnan - Sarı, Ramazan. “On Quasi-Conformal Flat Para-Sasakian Manifolds”. Turkish Journal of Mathematics and Computer Science 12/2 (Aralık 2020), 86-91. https://doi.org/10.47000/tjmcs.765297.
JAMA Ünal İ, Sarı R. On Quasi-Conformal Flat Para-Sasakian Manifolds. TJMCS. 2020;12:86–91.
MLA Ünal, İnan ve Ramazan Sarı. “On Quasi-Conformal Flat Para-Sasakian Manifolds”. Turkish Journal of Mathematics and Computer Science, c. 12, sy. 2, 2020, ss. 86-91, doi:10.47000/tjmcs.765297.
Vancouver Ünal İ, Sarı R. On Quasi-Conformal Flat Para-Sasakian Manifolds. TJMCS. 2020;12(2):86-91.