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Pseudo Conharmonically Symmetric Manifolds

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Abstract (2. Language): 
The object of the present paper is to study pseudo conharmonically symmetric manifold which is a type of non-flat Riemannian manifold. In the first section, we give the definition of a pseudo conharmonically symmetric manifold. In the second section, some theorems about this manifold are proved. In the last section, we give an example for the existence of this manifold.
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[1] D B Abdussatter. On conharmonic transformations in general relativity. Bulletin of Calcutta Mathematical Society, 41:409-416, 1966.
[ 2] T Adati and T Miyazawa. On a riemannian space with recurrent conformal curvature. The Tensor Society. Tensor. New Series, 18:348-354, 1967.
[3] E Cartan. Surune classe remarquable d' espaces de riemannian. Bulletin de la Societe Mathematique de France, 54:214-264, 1926.
[4] M C Chaki. On pseudo symmetric manifolds. Analele Stiintifice ale Universitatii Al. I. Cuza din Iasi, 33:53-58, 1987.
[5] M C Chaki and B Gupta. On conformally symmetric spaces. Indian Journal of Mathematics, 5:113-295, 1963.
[6] U C De and S Bandyopadhyay. On weakly symmetric riemannian spaces. Publicationes Mathematicae Debrecen, 54:371-381, 1999.
[7] U C De and S Bandyopadhyay. On weakly symmetric spaces. Acta Mathematics Hungarica, 83:205-212, 2000.
[ 8] U C De and A De. On almost pseudo-conformally symmetric ricci-recurrent manifolds with applications to relativity. Czechoslovak Mathematical Journal, 62(137):1055-1072,
2012.
[ 9] U C De and S Mallick. On almost pseudo concircularly symmetric manifolds. The Journal ofMathematics and Computer Science, 4(3):317-330, 2012.
[10] R Deszcz and W Grycak. On some class of warped product manifolds. Bulletin of the Institute ofMathematics. Academia Sinica, 15:311-322, 1987.
[11] S K Hui, A A Shaikh, and I Roy. On totaly umbilical hypersurfaces of weakly conharmonically symmetric spaces. Indian Journal of Pure and Applied Mathematics, 10(4):28-31,
2010.
[12] K Olszak and Z Olszak. On pseudo-riemannian manifolds with recurrent concircular curvature tensor. Acta Mathematica Hungar, 137(1-2):64-71, 2012.
[13] B O'Neill. Semi-riemannian geometry with applications to the relativity. Academic Press,
New York-London, 1983.
[14] F Özen and S Altay. On weakly and pseudo symmetric riemannian spaces. Indian Journal of Pure and Applied Mathematics, 33(10):1477-1488, 2001.
REFERENCES
255
[15] F Özen and S Altay. On weakly and pseudo concircular symmetric structures on a rieman-nian manifold. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, 47:129-138, 2008.
[16] M Prvanovic. On weakly symmetric riemannian manifolds. Publicationes Mathematicae Debrecen, 46:19-25, 1995.
[17] M Prvanovic. On totally umbilical submanifolds immersed in a weakly symmetric rie-mannian manifolds. Publicationes Mathematicae Debrecen, 6:54-64, 1998.
[18] W Roter. On conformally symmetric ricci-recurrent spaces. Colloquium Mathematicum,
31:87-96, 1974.
[19] A A Shaikh and S K Hui. On weakly conharmonically symmetric manifolds. The Tensor Society. Tensor. New Series, 70:119-134, 2008.
[ 20] S A Siddiqui and Z Ahsan. Conharmonic curvature tensor and the spacetime of general relativity. Differential Geometry-Dynamical Systems, 12:213-220, 2010.
[21] G Soos. Uber die geodatischen abbildungen von riemannschen raumen auf projektiv symmetrische remannsche raume. Acta Mathematica Academiae Scientiarum Hungaricae,
9:359-361, 1958.
[22] Z I Szabo. Structure theorems on riemannian spaces satisfying r(x,y)r=0. Journal of Differential Geometry, 17:531-582, 1982.
[23] L Tamassy and T Q Binh. On weakly symmetric and weakly projectively symmetric rie-mannian manifolds. Colloquia Mathematica Societatis Janos Bolyai, 56:663-670, 1989.
[ 24] A G Walker. On ruse' s space of recurrent curvature. Proceedings ofthe London Mathe¬matical Society, 52:36-64, 1951.
[ 25 ] H B Yilmaz. On decomposable almost pseudo conharmonically symmetric manifolds. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, 51(1):111-124, 2012.

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