Related papers: Multiply Warped Products with Non-Smooth Metrics
In this paper, we introduce semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms on singular semi-Riemannian manifolds. Semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms and their…
In this paper, we shall prove that space-like surfaces with bounded mean curvature functions in real analytic Lorentzian 3-manifolds can change their causality to time-like surfaces only if the mean curvature functions tend to zero.…
We examine biharmonic submanifolds within warped product structures. For a submanifold $(M,g)\subset (N,h)$ and a positive smooth function $f:I\to\mathbb{R}^+$, we study the inclusion $\varphi:(I\times M,\widetilde{g})\to (I\times…
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 work, we obtain a geometric description of surfaces $M^2$ of arbitrary codimension in the warped product $\mathbb{R}\times_\rho\mathbb{Q}^n_\epsilon$, with parallel mean curvature vector field in the normal connection, extending a…
We give necessary and sufficient conditions for warped product manifolds with 1-dimensional base, and in particular, for generalized Robertson-Walker spacetimes, to satisfy some generalized Einstein metric condition. We also construct…
We give a Riccati type formula adapted for two metrics having the same geodesics rays starting from a point or orthogonal to an hypersurface, one of these metrics being a warped product if the dimension $n$ is greater than or equal to 3.…
We derive one unified formula for Ricci curvature tensor on arbitrary warped product manifold by introducing a new notation for the lift vector and the Levi-Civita connection.This formula is helpful to further consider Ricci flow (RF) and…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
We present a coordinate free approach to derive curvature formulas for pseudo-Riemannian doubly warped product manifolds in terms of curvatures of their submanifolds. We also state the geodesics equation.
The main scalar-mean extremality and rigidity results in the existing literature concern manifolds whose curvature operators are nonnegative, or warped product spaces with a log-concave warping function whose leaves carry metrics of…
We study the problem of existence of isoperimetric regions for large volumes, in $C^0$-locally asymptotically Euclidean Riemannian manifolds with a finite number of $C^0$-asymptotically Schwarzschild ends. Then we give a geometric…
We establish metrics of positive $2^\mathrm{nd}$-intermediate Ricci curvature, i.e. $\mathrm{Ric}_2>0$, on products of positively curved homogeneous spaces. Using these examples, we demonstrate that the Hopf conjectures, Petersen-Wilhelm…
We solve spacelike spherically symmetric constant mean curvature (SS-CMC) hypersurfaces in Schwarzschild spacetimes and analyze their asymptotic behavior near the coordinate singularity r = 2M. Furthermore, we join SS-CMC hypersurfaces in…
We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics.…
This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality…
The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the…
In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, S. and Zhao (2018), with another "warping", one that is consistent with static spacetimes. We will give the PDE characterization for…
The aim of this paper is to extend classic results of the theory of CMC surfaces in the product spaces to the class of immersed surfaces in $\mathbb{M}^2(\kappa)\times\mathbb{R}$ whose mean curvature is given as a $C^1$ function depending…
We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.