\(W_2\)-curvature tensor on generalized Sasakian space forms
-
Venkatesha
vensmath@gmail.com
-
Shanmukha B.
meshanmukha@gmail.com
Downloads
DOI:
https://doi.org/10.4067/S0719-06462018000100017Abstract
In this paper, we study W2-pseudosymmetric, W2-locally symmetric, W2-locally φ- symmetric and W2-φ-recurrent generalized Sasakian space form. Further, illustrative examples are given.
Keywords
1] P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian space forms. Israel J. Math., 141 (2004), 157–183.
[2] P. Alegre and A. Carriazo, Structures on generalized Sasakian space forms. Differential Geometry and its Applications, 26 (2008), 656–666.
[3] P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian space forms. Taiwanese J. Math., 13 (2009), 923–941.
[4] P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal change of metric. Results Math., 59 (2011), 485–493.
[5] D. E. Blair, Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics Springer-Verlag, Berlin 509 (1976).
[6] D. E. Blair, Riemannian geometry of contact and symplectic manifolds. Birkha¨user Boston, 2002.
[7] M. C. Chaki, On pseudo symmetric manifolds. Ann.St.Univ.Al I Cuza Iasi, 33 (1987).
[8] U. C. De, A. Yildiz and A. F. Yaliniz, On φ-recurrent Kenmotsu manifolds. Turk J. Math., 33 (2009), 17–25.
[9] U. C. De and P. Majhi, φ-Semisymmetric generalized Sasakian space forms. Arab Journal of Mathematical Science, 21 (2015), 170–178.
[10] U. C. De and A. Sarkar, On projective curvature tensor of generelized Sasakian space forms. Quaestionens Mathematica, 33 (2010), 245–252.
[11] U. C. De, A. Shaikh and B. Sudipta, On φ-recurrent Sasakian manifolds. Novi Sad J.Math., 33 (13) (2003), 43–48.
[12] R. Deszcz, On pseudosymmetric spaces. Bull. Soc. Math. Belg. Ser. A, 44 (1992), 1–34.
[13] S. K. Hui and D. Chakraborty, Generalized Sasakian space forms and Ricci almost solitons with a conformal Killing vector field, New Trends Math. Sci., 4(3) (2016), 263–269.
[14] U. K. Kim, Conformally flat generalised Sasakian space forms and locally symmetric Generalized Sasakian space forms. Note di mathematica, 26 (2006), 55–67.
[15] G. P. Pokhariyal, Study of a new curvature tensor in a Sasakian manifold. Tensor N.S., 36(2) (1982), 222–225.
[16] G. P. Pokhariyal and R. S. Mishra, The curvature tensor and their relativistic significance. Yokohoma Mathematical Journal, 18 (1970), 105–108.
[17] D. G. Prakash, On generalized Sasakian Space forms with Weyl conformal Curvature tensor. Lobachevskii Journal of Mathematics, 33(3) (2012), 223–228.
[18] A. Sarkar and A. Akbar, Generalized Sasakian space forms with Projective Curvature tensor. Demonstratio Math., 47(3) (2014), 725–735.
[19] A. Sarkar and M. Sen, On φ-Recurrent generalized Sasakian space forms. Lobachevskii Journal of Mathematics, 33(3) (2012), 244–248.
[20] A. A. Shaikh, T. Basu and S. Eyasmin, On the Existence of φ-recurrent (LCS)n-manifolds. extracta mathematicae, 23 (2008), 71-83.
[21] B. Shanmukha and Venkatesha, Some results on generalized Sasakian space forms with quarter symmetric metric connection. Asian Journal of Mathematics and Computer Research 25(3) 2018, 183-191.
[22] B. Shanmukha, Venkatesha and S. V. Vishunuvardhana, Some Results on Generalized (k, µ)- space forms. New Trends Math. Sci., 6(3) 2018, 48-56.
[23] S. Sasaki, Lecture note on almost Contact manifolds. Part-I, Tohoku University, 1965.
[24] R. N. Singh and S. K. Pandey, On generalized Sasakian space forms. The Mathematics Student, 81 (2012), 205–213.
[25] R. N. Singh and G. Pandey On W2-curvature tensor of the semi symmetric non- metric connection in a Kenmotsu manifold. Novi Sad J. Math., 43 (2) 2013, 91–105.
[26] J. P. Singh, Generalized Sasakian space forms with m-Projective Curvature tensor. Acta Math. Univ. Comenianae, 85(1) (2016), 135–146.
[27] Z. I. Szabo, Structure theorem on Riemannian space satisfying (R(X, Y) · R) = 0. I. the local version. J. Differential Geom., 17 (1982), 531–582.
[28] T. Takahashi, Sasakian φ-symmetric space. Tohoku Math.J., 29 (91) (1977), 91–113.
[29] Venkatesha and C. S. Bagewadi, On concircular φ-recurrent LP-Sasakian manifolds. Differential Geometry Dynamical Systems, 10 (2008), 312–319.
[30] Venkatesha, C. S. Bagewadi and K. T. Pradeep Kumar Some Results on Lorentzian Para-Sasakian Manifolds International Scholarly Research Network Geometry 2011, doi:10.5402/2011/161523.
[31] Venkatesha and B. Sumangala, on M-projective curvature tensor of generalised Sasakian space form. Acta Math. Univ. Comenianae, 2 (2013), 209–217.
[2] P. Alegre and A. Carriazo, Structures on generalized Sasakian space forms. Differential Geometry and its Applications, 26 (2008), 656–666.
[3] P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian space forms. Taiwanese J. Math., 13 (2009), 923–941.
[4] P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal change of metric. Results Math., 59 (2011), 485–493.
[5] D. E. Blair, Contact manifolds in Riemannian geometry. Lecture Notes in Mathematics Springer-Verlag, Berlin 509 (1976).
[6] D. E. Blair, Riemannian geometry of contact and symplectic manifolds. Birkha¨user Boston, 2002.
[7] M. C. Chaki, On pseudo symmetric manifolds. Ann.St.Univ.Al I Cuza Iasi, 33 (1987).
[8] U. C. De, A. Yildiz and A. F. Yaliniz, On φ-recurrent Kenmotsu manifolds. Turk J. Math., 33 (2009), 17–25.
[9] U. C. De and P. Majhi, φ-Semisymmetric generalized Sasakian space forms. Arab Journal of Mathematical Science, 21 (2015), 170–178.
[10] U. C. De and A. Sarkar, On projective curvature tensor of generelized Sasakian space forms. Quaestionens Mathematica, 33 (2010), 245–252.
[11] U. C. De, A. Shaikh and B. Sudipta, On φ-recurrent Sasakian manifolds. Novi Sad J.Math., 33 (13) (2003), 43–48.
[12] R. Deszcz, On pseudosymmetric spaces. Bull. Soc. Math. Belg. Ser. A, 44 (1992), 1–34.
[13] S. K. Hui and D. Chakraborty, Generalized Sasakian space forms and Ricci almost solitons with a conformal Killing vector field, New Trends Math. Sci., 4(3) (2016), 263–269.
[14] U. K. Kim, Conformally flat generalised Sasakian space forms and locally symmetric Generalized Sasakian space forms. Note di mathematica, 26 (2006), 55–67.
[15] G. P. Pokhariyal, Study of a new curvature tensor in a Sasakian manifold. Tensor N.S., 36(2) (1982), 222–225.
[16] G. P. Pokhariyal and R. S. Mishra, The curvature tensor and their relativistic significance. Yokohoma Mathematical Journal, 18 (1970), 105–108.
[17] D. G. Prakash, On generalized Sasakian Space forms with Weyl conformal Curvature tensor. Lobachevskii Journal of Mathematics, 33(3) (2012), 223–228.
[18] A. Sarkar and A. Akbar, Generalized Sasakian space forms with Projective Curvature tensor. Demonstratio Math., 47(3) (2014), 725–735.
[19] A. Sarkar and M. Sen, On φ-Recurrent generalized Sasakian space forms. Lobachevskii Journal of Mathematics, 33(3) (2012), 244–248.
[20] A. A. Shaikh, T. Basu and S. Eyasmin, On the Existence of φ-recurrent (LCS)n-manifolds. extracta mathematicae, 23 (2008), 71-83.
[21] B. Shanmukha and Venkatesha, Some results on generalized Sasakian space forms with quarter symmetric metric connection. Asian Journal of Mathematics and Computer Research 25(3) 2018, 183-191.
[22] B. Shanmukha, Venkatesha and S. V. Vishunuvardhana, Some Results on Generalized (k, µ)- space forms. New Trends Math. Sci., 6(3) 2018, 48-56.
[23] S. Sasaki, Lecture note on almost Contact manifolds. Part-I, Tohoku University, 1965.
[24] R. N. Singh and S. K. Pandey, On generalized Sasakian space forms. The Mathematics Student, 81 (2012), 205–213.
[25] R. N. Singh and G. Pandey On W2-curvature tensor of the semi symmetric non- metric connection in a Kenmotsu manifold. Novi Sad J. Math., 43 (2) 2013, 91–105.
[26] J. P. Singh, Generalized Sasakian space forms with m-Projective Curvature tensor. Acta Math. Univ. Comenianae, 85(1) (2016), 135–146.
[27] Z. I. Szabo, Structure theorem on Riemannian space satisfying (R(X, Y) · R) = 0. I. the local version. J. Differential Geom., 17 (1982), 531–582.
[28] T. Takahashi, Sasakian φ-symmetric space. Tohoku Math.J., 29 (91) (1977), 91–113.
[29] Venkatesha and C. S. Bagewadi, On concircular φ-recurrent LP-Sasakian manifolds. Differential Geometry Dynamical Systems, 10 (2008), 312–319.
[30] Venkatesha, C. S. Bagewadi and K. T. Pradeep Kumar Some Results on Lorentzian Para-Sasakian Manifolds International Scholarly Research Network Geometry 2011, doi:10.5402/2011/161523.
[31] Venkatesha and B. Sumangala, on M-projective curvature tensor of generalised Sasakian space form. Acta Math. Univ. Comenianae, 2 (2013), 209–217.
Most read articles by the same author(s)
- D. G. Prakasha, H. Harish, P. Veeresha, Venkatesha, The Zamkovoy canonical paracontact connection on a para-Kenmotsu manifold , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- Vishnuvardhana S.V., Venkatesha, Results on para-Sasakian manifold admitting a quarter symmetric metric connection , CUBO, A Mathematical Journal: Vol. 22 No. 2 (2020)
- G. Divyashree, Venkatesha, Certain results on the conharmonic curvature tensor of \( (\kappa,\mu) \)-contact metric manifolds , CUBO, A Mathematical Journal: Vol. 22 No. 1 (2020)
- Venkatesha, Divyashree G., Three dimensional f-Kenmotsu manifold satisfying certain curvature conditions , CUBO, A Mathematical Journal: Vol. 19 No. 1 (2017): CUBO, A Mathematical Journal
Downloads
Download data is not yet available.
Published
2018-10-19
How to Cite
[1]
Venkatesha and S. B., “\(W_2\)-curvature tensor on generalized Sasakian space forms”, CUBO, vol. 20, no. 1, pp. 17–29, Oct. 2018.
Issue
Section
Articles
