Research Article

Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions

Volume: 6 Number: 2 October 31, 2018
EN

Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions

Abstract

The object of the present paper is to study some classes of 3-dimensional quasi-para-Sasakian manifolds
with  beta=const. We investigated 3-dimensional quasi-para-Sasakian manifolds with beta=const. satisfying
the curvature conditions P:Q = 0; Q:P = 0; P:R = 0, where P is the projective curvature tensor, Q is
the Ricci operator and R is the Riemannian curvature tensor. Also, a 3-dimensional concircularly flat
quasi-para-Sasakian manifold with  beta=const. is studied. Finally, an example of 3-dimensional proper
quasi-para-Sasakian manifold with  beta =const. is given.

Keywords

quasi-para-Sasakian manifold,Einstein manifold,concircularly flat,Projective curvature tensor

References

  1. [1] Bejan, C. L. and Crasmareanu M., Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom. 46(2) (2014), 117–127.
  2. [2] Besse, A. L., Einstein manifolds, Springer-verlag, Berlin-Heidelberg (1987).
  3. [3] Blair, D. E., The theory of quasi-Sasakian structures, J. Differential Geom. 1 (1967), 331–345.
  4. [4] Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics Vol. 203, Birkhäuser, Boston, 2002.
  5. [5] Cappelletti-Montano, B., Küpeli Erken, I. and Murathan, C., Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665–693.
  6. [6] Dacko, P., On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193–213.
  7. [7] Deszcz, R., Verstraelen L. and Yaprak S.,Warped products realizing a certain conditions of pseudosymmetry type imposed on theWeyl curvature tensor, Chin. J. Math. 22(1994), 139-157.
  8. [8] Erdem, S., On almost (para)contact (hyperbolic) metric manifolds and harmonicity of ('; '0)- holomorphic maps between them, Houston J. Math. 28 (2002), 21–45.
  9. [9] Kanemaki, S., Quasi-Sasakian manifolds, Tohoku Math. J. 29 (1977), 227–233.
  10. [10] Kaneyuki, S. and Williams, F. L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J 1985; 99: 173–187.
APA
Küpeli Erken, İ. (2018). Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Mathematical Sciences and Applications E-Notes, 6(2), 57-65. https://izlik.org/JA79EJ86GA
AMA
1.Küpeli Erken İ. Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Math. Sci. Appl. E-Notes. 2018;6(2):57-65. https://izlik.org/JA79EJ86GA
Chicago
Küpeli Erken, İrem. 2018. “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”. Mathematical Sciences and Applications E-Notes 6 (2): 57-65. https://izlik.org/JA79EJ86GA.
EndNote
Küpeli Erken İ (October 1, 2018) Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Mathematical Sciences and Applications E-Notes 6 2 57–65.
IEEE
[1]İ. Küpeli Erken, “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 57–65, Oct. 2018, [Online]. Available: https://izlik.org/JA79EJ86GA
ISNAD
Küpeli Erken, İrem. “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”. Mathematical Sciences and Applications E-Notes 6/2 (October 1, 2018): 57-65. https://izlik.org/JA79EJ86GA.
JAMA
1.Küpeli Erken İ. Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Math. Sci. Appl. E-Notes. 2018;6:57–65.
MLA
Küpeli Erken, İrem. “Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, Oct. 2018, pp. 57-65, https://izlik.org/JA79EJ86GA.
Vancouver
1.İrem Küpeli Erken. Three Dimensional Quasi-Para-Sasakian Manifolds Satisfying Certain Curvature Conditions. Math. Sci. Appl. E-Notes [Internet]. 2018 Oct. 1;6(2):57-65. Available from: https://izlik.org/JA79EJ86GA