Related papers: Serrin's type problems in warped product manifolds

We prove some results of Kemperman--Scherk type for restricted product sets in multiplicative groups of fields (in particular, for cyclic groups). The proofs use polynomial method.

We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation…

In this paper, we define the semi-symmetric metric connection on super Riemannian manifolds. We compute the semi-symmetric metric connection and its curvature tensor and its Ricci tensor on super warped product spaces. We introduce two kind…

By applying an average method in PDE, we obtain a dichotomy between "constancy" and "infinity" of the warping functions on complete noncompact Riemannian manifolds for an appropriate isometric immersion of a multiply warped product manifold…

In this paper, we introduce the notion of warped product quasi bi-slant submanifolds in Kaehler manifolds. We have shown that every warped product quasi bi-slant submanifold in a Kaehler manifold is either a Riemannian product or a warped…

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures…

The purpose of this paper is to study pointwise pseudo-slant warped product submanifolds of a K\"{a}hler manifold $\widetilde{M}$. We derive the conditions of integrability and totally geodesic foliation for the distributions allied to the…

In this paper, we prove the existence of hypersurfaces in the Euclidean space with prescribed boundary and whose k-th Weingarten curvature equals a given function that depends on the normal of the hypersurface. The proof is based on the…

Generalized Roter type manifold is a generalization of conformally flat manifold as well as Roter type manifold, which gives rise the form of the curvature tensor in terms of algebraic combinations of the fundamental metric tensor and Ricci…

In this paper we study gradient Ricci-Harmonic soliton with structure of warped product manifold. We obtain some triviality results for the potential function, warping function and the harmonic map which reaches maximum or minimum. In order…

In this paper we aim at characterizing the gauge balls in the Heisenberg group $\mathbb{H}^n$ as the only domains where suitable overdetermined problems of Serrin type can be solved. We discuss a one parameter family of overdetermined…

In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the…

The Serre problem for a class of hyperbolic pseudoconvex Reinhardt domains in $\Bbb C^2$ as fibers is solved.

We prove triviality results for Einstein warped products with non-compact bases. These extend previous work by D.-S. Kim and Y.-H. Kim. The proof, from the viewpoint of "quasi-Einstein manifolds" introduced by J. Case, Y.-S. Shu and G. Wei,…

In this work, transverse shear warping functions for an equivalent single layer plate model are formulated from a variational approach. The part of the strain energy which involves the shear phenomenon is expressed in function of the…

We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.

We consider the curvature of a family of warped products of two pseduo-Riemannian manifolds $(B,g_B)$ and $(F,g_F)$ furnished with metrics of the form $c^{2}g_B \oplus w^2 g_F$ and, in particular, of the type $w^{2 \mu}g_B \oplus w^2 g_F$,…

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

In this paper we prove the scalar curvature extremality and rigidity for a class of warped product spaces that are possibly degenerate at the two ends. The leaves of these warped product spaces can be any closed Riemannian manifolds with…

This is a survey about the contruction of warped products between (semi-)Riemannian manifolds and metric (measure) spaces. The resulting spaces will be semi-Riemannian manifolds, metric (measure) spaces or Lorentzian metric and metric…