A multidimensional gravitational model with several scalar fields, fields of forms and cosmological constant is considered. When scalar fields are constant and composite p-brane monopole-like ansatz for the fields of forms is adopted, a wide class of solutions on product of n + 1 Einstein spaces is obtained. These solutions are composite p-brane generalizations of the Freund-Rubin solution. Som...

The product of two free scalar fields on a manifold is shown to be a well defined operator valued distribution on the GNS Hilbert space of a globally Hadamard product state. Viewed as a new field all n-point distributions exist, giving a new example for a Wightman field on a manifold.

Abstract For a closed, connected direct product Riemannian manifold $$(M, g)=(M_1, g_1) \times \cdots (M_l, g_l)$$ ( M , g ) = 1 × ⋯ <mml:mi...

In this paper we study Riemannian manifolds (M, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling can be adapted to this setting. As a by-product, we define a family of scalar curvatures, one of which corresponds to Perelman’s scalar curvature function. We also study the variational problem nat...

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

In this paper we continue to study Riemannian manifolds (M, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling can be adapted to this setting. As a by-product, we define a family of scalar curvatures, one of which corresponds to Perelman’s scalar curvature function. We also study the variational...

This paper proposes to go beyond the Einstein General Relativity theory in a noncommutative geometric framework. As first step, we rewrite intrinsically (coordinate-free formulation). second and Bianchi identities, including torsion, within minimal algebraic hypotheses. Then, order extend for dealing with scalar fields on manifold $$\mathcal {M}$$ , are forced adapt definition of vector connect...