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ON TRANS-SASAKIAN MANIFOLD EQUIPPED WITH m-PROJECTIVE CURVATURE TENSOR

Yıl 2017, Cilt: 7 Sayı: 2, 282 - 290, 01.12.2017

Öz

The work towards of the attending paper is to interpret the trans-Sasakian manifold equipped with m-projective curvature tensor and its various geometric proper- ties. First, we observe that m-projectively at trans-Sasakian manifold is Einstein. In order, we discussed m-projectively conservative and -m-projectively at trans-Sasakian manifold. Following, we found the sucient condition for quasi m-projectively at trans- Sasakian manifold to be m-projectively at. In the end, the m-projectively and -m- projectively symmetric trans-Sasakian manifolds are analyzed.

Kaynakça

  • Blair,D.E., (1976), Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer Verlag.
  • Cartan,E., (1926), Sur une classes remarquable d’espaces de Riemann, Bull. Soc. Math. France, 54, pp.214-26.
  • Chaubey,S.K. and Ojha,R.H., (2010), On the m-projective curvature tensor of a Kenmotsu manifold, Diff. Geom. Dyn. Sys., 12, pp.52-60.
  • De,U.C. and Shaikh,A.A., (2009), Complex manifolds and contact manifolds, Narosa Publication, New Delhi, India.
  • Hicks,N.J., (1969), Notes on Differential Geometry, Affiliated East West Press Pvt. Ltd.
  • Ojha,R.H., (1975), A note on the mprojective curvature tensor, Indian J. Pure Appl. Math., 8 (12), pp.1531-1534.
  • Ojha,R.H., (1986), m-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math., 17 (4), pp.1531-1534.
  • Oubina,J.A., (1985), New classes of almost contact metric structures, Publ. Math. Debrecen, 32, pp.21-38.
  • Pokhariyal,G.P. and Mishra,R.S., (1971), Curvature tensors and their relativistic significance-ii, Yoko- hama Math. J., 19, pp.97-103.
  • Prakash,A., Ahmad,M., and Srivastava,A., (2013), m-projective curvature tensors on a LP-Sasakian manifolds, IOSR J. Math., 6, pp.19-23.
  • Prasad,R. and Srivastava,V., (2013), Some results on trans-Sasakian manifolds, Math. Vesnik, 65, pp.346-352.
  • Singh,J.P., (2015), On the M -projective curvature tensor of Sasakian manifold, Sci. Vis., 15 (2), pp.76-79.
  • Takahashi,T., (1977), Sasakian φ-symmetric space, Tohoku Math. J., 29, pp.91-113.
  • Tamassy,L. and Binh,T.Q., (1989), On weakly symmetric and weakly projective symmetric Riemann- ian manifold, Colloquia Math. Soc., 50, pp.663-667.
  • Zengin,F.O., (2013), On m-projectively flat LP-Sasakian manifolds, Ukr. Math. J., 65, pp.1725-1732.
Yıl 2017, Cilt: 7 Sayı: 2, 282 - 290, 01.12.2017

Öz

Kaynakça

  • Blair,D.E., (1976), Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer Verlag.
  • Cartan,E., (1926), Sur une classes remarquable d’espaces de Riemann, Bull. Soc. Math. France, 54, pp.214-26.
  • Chaubey,S.K. and Ojha,R.H., (2010), On the m-projective curvature tensor of a Kenmotsu manifold, Diff. Geom. Dyn. Sys., 12, pp.52-60.
  • De,U.C. and Shaikh,A.A., (2009), Complex manifolds and contact manifolds, Narosa Publication, New Delhi, India.
  • Hicks,N.J., (1969), Notes on Differential Geometry, Affiliated East West Press Pvt. Ltd.
  • Ojha,R.H., (1975), A note on the mprojective curvature tensor, Indian J. Pure Appl. Math., 8 (12), pp.1531-1534.
  • Ojha,R.H., (1986), m-projectively flat Sasakian manifolds, Indian J. Pure Appl. Math., 17 (4), pp.1531-1534.
  • Oubina,J.A., (1985), New classes of almost contact metric structures, Publ. Math. Debrecen, 32, pp.21-38.
  • Pokhariyal,G.P. and Mishra,R.S., (1971), Curvature tensors and their relativistic significance-ii, Yoko- hama Math. J., 19, pp.97-103.
  • Prakash,A., Ahmad,M., and Srivastava,A., (2013), m-projective curvature tensors on a LP-Sasakian manifolds, IOSR J. Math., 6, pp.19-23.
  • Prasad,R. and Srivastava,V., (2013), Some results on trans-Sasakian manifolds, Math. Vesnik, 65, pp.346-352.
  • Singh,J.P., (2015), On the M -projective curvature tensor of Sasakian manifold, Sci. Vis., 15 (2), pp.76-79.
  • Takahashi,T., (1977), Sasakian φ-symmetric space, Tohoku Math. J., 29, pp.91-113.
  • Tamassy,L. and Binh,T.Q., (1989), On weakly symmetric and weakly projective symmetric Riemann- ian manifold, Colloquia Math. Soc., 50, pp.663-667.
  • Zengin,F.O., (2013), On m-projectively flat LP-Sasakian manifolds, Ukr. Math. J., 65, pp.1725-1732.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

J. P. Jaiswal Bu kişi benim

A. S. Yadav Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 2

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