Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 28, No. 2, pp. 197-206 (2012)

Generalized warped product manifolds and critical Riemannian metric

Djaa Nour El Houda and Djaa Mustapha

University of Relizane

Abstract: In this paper, we present some properties of generalized warped product manifold. We establish the relationship between the scalar curvature of a generalized warped product $M\times_{f} N$ of Riemannian manifolds and those ones of $M$ an $ N$, and we obtain a necessary condition for a critical Riemannian metrics on $M\times_{f} N$.

Keywords: warped product manifolds, scalar curvature, critical metric

Classification (MSC2000): 53A30; 53B20, 53C21

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