Pseudo Projective Tensor of Almost Kahler Manifold

Wissam Abbas Hussein; Rawah A. Zaben

doi:10.51699/cajotas.v7i3.1735

Authors

Wissam Abbas Hussein General Directorate of Education of Salahuddin, Salahuddin, Iraq
Rawah A. Zaben Salah Al-Deen's Education, The Ministry of Education, Iraq

DOI:

https://doi.org/10.51699/cajotas.v7i3.1735

Keywords:

Almost Kahler, Ricci Tensor, Pseudo Projective Tensor

Abstract

The work from this research is to analyze the mathematical aspects of conharmonic tensor of projective Almost Kahler manifold. We get the Almost Kahler’s manifold composites of the projecting tensor by using the cylindrical characteristics of the projected curvature tensor. And discovered several Kahler-like projective elements. Finally, demonstrated that the projections Almost Kahlar manifold's flat holomorphic sectional tensor is the manifold M. and shown that M is a Kahler manifold.

Downloads

Download data is not yet available.

References

A. Gray, “Minimal varieties and almost Hermitian submanifolds,” Michigan Mathematical Journal, vol. 12, pp. 273–279, 1965.

P. K. Rachevski, Riemannian Geometry and Tensor Analysis. Moscow, Russia: Nauka, 1964.

A. Lichnerowicz, Théorie Globale des Connexions et des Groupes d’Holonomie. Rome, Italy: Edizioni Cremonese, 1955.

V. F. Kirichenko, New Results of K-Spaces Theory, Ph.D. dissertation, Moscow State University, Moscow, Russia, 1975.

H. A. Rakees, Locally Conformal Kähler Manifold of Class R, M.S. thesis, College of Science, University of Basrah, Basrah, Iraq, 2004.

J. M. Jawad, Almost Kähler Manifold of Class R₁, M.S. thesis, College of Science, University of Basrah, Basrah, Iraq, 2004.

S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. 1. New York, NY, USA: John Wiley & Sons, 1963.

U. Yildirim, M. Atceken, and S. Dirik, “Pseudo-projective curvature tensor satisfying some properties on a normal paracontact metric manifold,” Communications Faculty of Sciences University of Ankara, Series A1: Mathematics and Statistics, vol. 68, no. 1, pp. 997–1016, 2019.

S. Koto, “Some theorems on almost Kählerian spaces,” Journal of the Mathematical Society of Japan, vol. 12, pp. 422–433, 1960.

V. F. Kirichenko, Theory of Lie Groups. Tver, Russia: Tver State University, 1995.

V. F. Kirichenko, “K-spaces of constant type,” Siberian Mathematical Journal, vol. 17, no. 2, pp. 282–289, 1976.

L. Ignatochkina, New Aspects of Geometry of Vaisman–Gray Manifold, Ph.D. dissertation, Moscow State Pedagogical University, Moscow, Russia, 2001.

R. N. Singh and S. K. Pandey, “On the M-projective curvature tensor of N(k)-contact metric manifolds,” vol. 2013, Art. no. 932564, 2013.

A. Gray, “Nearly Kähler manifolds,” Journal of Differential Geometry, vol. 4, pp. 283–309, 1970.

M. Jawarneh and Samui, “Projective curvature tensor on (k, μ)-contact space forms,” Journal of Pure and Applied Mathematics, vol. 113, no. 3, pp. 425–439, 2017.

A. Shihab, V. F. Kirichenko, and A. Rustanov, “On geometry of the tensor of conharmonic curvature of almost Hermitian manifolds,” Mathematical Notes, vol. 90, no. 1, pp. 87–103, 2011.

B. Prasad, “A pseudo-projective curvature tensor on a Riemannian manifold,” Bulletin of the Calcutta Mathematical Society, vol. 94, no. 3, pp. 163–166, 2002.

A. Z. Petrov, Einstein Spaces. Moscow, Russia: Physico-Mathematical Literature, 1961.

C. S. Bagewadi, D. G. Prakasha, and Venkatesha, “On pseudo-projectively flat LP-Sasakian manifold with a coefficient α,” Annales Universitatis Mariae Curie-Skłodowska, vol. 61, pp. 1–8, 2007.