Related papers: The Warped Product of Hamiltonian Spaces

In this paper, we introduce horizontal and vertical warped product Finsler manifold. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemmanian…

In this paper we review $G_2$ and $Spin(7)$ geometries in relation with a special type of metric structure which we call warped-like product metric. We present a general ansatz of warped-like product metric as a definition of warped-like…

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped…

In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…

We study Einstein riemannian manifolds endowed with a warped product structure. We focus on the case in which both the base and the fiber are Einstein manifolds and establish necessary and sufficient conditions for the warped product itself…

Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first…

We study Einstein warped space with a quarter symmetric connection. As a result, first, we find basic results on curvature, Ricci and scalar tensors with respect to the quarter symmetric connection. Moreover, we prove some results…

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…

We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: - the characterization of the Sobolev spaces in such products - the proof that, under natural…

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…

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 prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…

We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be…

Noting that the complete lift of a Rimannian metric defined on a differentiable manifold is not 0-homogeneous on the fibers of the tangent bundle . In this paper we introduce a new lift which is 0-homogeneous. It determines on slit tangent…

The warped product $N_1\times_f N_2$ of two Riemannian manifolds $(N_1,g_1)$ and $(N_2,g_2)$ is the product manifold $N_1\times N_2$ equipped with the warped product metric $g=g_1+f^2 g_2$, where $f$ is a positive function on $N_1$. The…

Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddings arising from warped product manifolds using the language…

In this paper we consider a class of Einstein warped product semi-Riemannian manifolds $\widehat{M} = M^{n}\times_{f}N^{m}$ with $n\geq 3$ and $m\geq 2$. For $\widehat{M}$ with compact base and Ricci-flat fiber, we prove that $\widehat{M}$…

In this paper, we generalize the dualistic structures on warped product manifolds to the dualistic structures on generalized warped product manifolds. we develop an expression of curvature for the connection of the generalized warped…

We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian…

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian…