The object of the present paper is to study weakly cyclic Z symmetric manifolds. Some geometric properties have been studied. We obtain a sufficient condition for a weakly cyclic Z symmetric manifold to be a quasi Einstein manifold. Next we consider conformally flat weakly cyclic Z symmetric manifolds. Then we study Einstein (WCZS)n (n > 2). Also we study decomposable (WCZS)n (n > 2). We prove the equivalency of semisymmetry and Weyl-semisymmetry in a (WCZS)n (n > 2). Finally, we give an example of a (WCZS)4.
On weakly cyclic Z symmetric manifolds / U.C. De, C.A. Mantica, Y.J. Suh. - In: ACTA MATHEMATICA HUNGARICA. - ISSN 0236-5294. - 146:1(2015 Jun), pp. 153-167. [10.1007/s10474-014-0462-9]
On weakly cyclic Z symmetric manifolds
C.A. Mantica
Secondo
;
2015
Abstract
The object of the present paper is to study weakly cyclic Z symmetric manifolds. Some geometric properties have been studied. We obtain a sufficient condition for a weakly cyclic Z symmetric manifold to be a quasi Einstein manifold. Next we consider conformally flat weakly cyclic Z symmetric manifolds. Then we study Einstein (WCZS)n (n > 2). Also we study decomposable (WCZS)n (n > 2). We prove the equivalency of semisymmetry and Weyl-semisymmetry in a (WCZS)n (n > 2). Finally, we give an example of a (WCZS)4.
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