Projectively Vanishing Nearly Cosymplectic Manifold

Authors

  • Habeeb M. Abood Department of Mathematics, University of Basrah, Basrah
  • Nawaf J. Mohammed Department of Mathematics, University of Basrah, Basrah

DOI:

https://doi.org/10.26713/cma.v9i2.692

Keywords:

Projective curvature tensor, Almost contact manifold, Nearly cosymplectic manifold

Abstract

The present paper focuses on the study of the geometric properties of projective curvature tensor on the nearly cosymplectic manifold. In particular, the flatness properties of projective tensor have been studied, so related to these properties we defined three special classes of nearly cosymplectic manifold.

Downloads

Download data is not yet available.

References

H.M. Abood, Holomorphic-Geodesic Transformation of Almost Hermitian Manifold, Ph.D. thesis, Moscow state university, Moscow (2002).

H.M. Abood and H.G. Abd Ali, Projective-recurrent Viasman-Gray manifold, Asian Journal of Mathematics and Computer Research 13 (3) (2016), 184 – 191.

H.M. Abood and N.J. Mohammed, Locally conformal Kahler manifold of pointwise holomorphic sectional curvature tensor, International Mathematical Forum 5 (45) (2010), 2213 – 2224.

M. Banaru, On nearly-cosymplectic hypersurfaces in nearly-Kahlerian Manifolds, Studia Univ. Babes - Bolyai. Math. Cluj - Napoca. 47 (3) (2002), 2 – 11.

D.E. Blair, The theory of quasi-Sasakian structures, J. Differential Geometry 1 (1967), 331 – 345.

D.E. Blair and D.K. Showers, Almost contact manifolds with Killing structure tensors I, Pacific J. Math. 39 (2) (1971), 285 – 292.

D.E. Blair and D.K. Showers, Almost contact manifolds with Killing structure tensors II, J. Differential Geometry 9 (1974), 577 – 582.

D.E. Blair, D.K. Showers and K. Yano, Nearly Sasakian structure, Kodoi Math. Sem. Rep. 27 (1-2) (1976), 175 – 180.

S. Chern, Pseudo-groups continues infins, Strasbourg. Colloq. International du C.N.R.S. 52 (1953), 119 – 136.

D. Chinea, Conformal changes of almost contact metric structures, Riv. Math. Univ. Parama. 1 (1992), 19 – 31.

D. Chinea and J. Marrero, Classification of almost contact metric structures, Rev. Romaine Math. Pures App. 37 (1992), 199 – 212.

H. Endo, On the curvature tensor of nearly cosymplectic manifolds of constant (Phi)-section curvature, An. Stin. Univ. Al. I. Cuza. Iasi. T. LI. 2 (2005), 439 – 454.

H. Endo, Remarks on nearly cosymplectic manifolds of constant (Phi)-section curvature with a submersion of geodesic fiber, Tensor. N.S.V. 66 (2005), 26 – 39.

S. Fueki and H. Endo, On conformally flat nearly cosymplectic manifolds, Tensor. N.S.V. 66 (2005), 305 – 316.

M. Jawarneh and S. Samui, Projective curvature tensor on ((k,mu))-contact space forms, Journal of Pure and Applied Mathematics 113 (3) (2017), 425 – 439.

V.F. Kirichenko, Differential geometry of K-space problems of geometry, Itogi Nauki i Tekhniki. Ser. Probl. Geom. 8 (1977), 139 – 161.

V.F. Kirichenko, The method of generalization of Hermitian geometry in the almost Hermitian contact manifold, Problems of Geometry VINITE ANSSR 18 (1986), 25 – 71.

V.F. Kirichenko, Differential- Geometry Structures on Manifolds, 2nd edition, Expanded Odessa, Printing House, p. 458 (2013).

V.F. Kirichenko and E.V. Kusova, On geometry of weakly cosympletic manifold, Journal of Mathematical Sciences 177 (2011), 668.

V.F. Kirichenko and A.R. Rustanov, Differential Geometry of quasi-Sasakian manifolds, Mathematical Collection 193(8) (2002), 71 – 100.

A.Z. Petrov, Einstein space, Phys-Math. Letr. Moscow (1961), p. 463.

P.K. Rachevski, Riemmanian geometry and tensor analysis, Uspekhi Mat. Nauk. 10 (4) (66) (1955), 219 – 222.

S. Sasaki, On the inegrability of almost contact structures, Tohoko Math. J. 14 (1962), 167 – 176.

Downloads

Published

30-06-2018
CITATION

How to Cite

Abood, H. M., & Mohammed, N. J. (2018). Projectively Vanishing Nearly Cosymplectic Manifold. Communications in Mathematics and Applications, 9(2), 207–217. https://doi.org/10.26713/cma.v9i2.692

Issue

Section

Research Article