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- Title
RECURRENT Z FORMS ON RIEMANNIAN AND KAEHLER MANIFOLDS.
- Authors
MANTICA, CARLO ALBERTO; SUH, YOUNG JIN
- Abstract
In this paper, we introduce a new kind of Riemannian manifold that generalize the concept of weakly Z-symmetric and pseudo-Z-symmetric manifolds. First a Z form associated to the Z tensor is defined. Then the notion of Z recurrent form is introduced. We take into consideration Riemannian manifolds in which the Z form is recurrent. This kind of manifold is named ()n. The main result of the paper is that the closedness property of the associated covector is achieved also for (Zkl) > 2. Thus the existence of a proper concircular vector in the conformally harmonic case and the form of the Ricci tensor are confirmed for()n manifolds with (Zkl) > 2. This includes and enlarges the corresponding results already proven for pseudo-Z-symmetric ()n and weakly Z-symmetric manifolds ()n in the case of non-singular Z tensor. In the last sections we study special conformally flat ()n and give a brief account of Z recurrent forms on Kaehler manifolds.
- Subjects
RIEMANNIAN manifolds; GENERALIZATION; MATHEMATICAL forms; SYMMETRY (Physics); HARMONIC analysis (Mathematics); APPLIED mathematics; EXISTENCE theorems
- Publication
International Journal of Geometric Methods in Modern Physics, 2012, Vol 9, Issue 7, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887812500594