arXiv research

The paper modifies a warped product space to find conditions for constant height functions.

Characterizes warping functions in Einstein Poisson warped spaces.

The paper proves rigidity for submanifolds in warped product manifolds.

The paper studies a new type of submanifolds in product spaces.

No proper biharmonic CMC compact hypersurface in a specific warped product space.

Defines semi-symmetric metric connection on super warped products.

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 the same up to scaling, while in the non-compact case there are simple examples …

Study information geometry of warped product spaces, finding special connections.

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 product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…

Study Einstein warped products with Einstein base and fiber.

The paper studies special warped products with a specific connection on super Riemannian manifolds.

Study on Riemannian Poisson warped product spaces and their properties.

Estimates mean curvature, scalar curvature, shape operator in warped products.

Study characterizes Einstein metrics in warped product spaces.

The paper proves rigidity for warped product spaces with degenerate ends.

In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar curvature. Then apply our results to generalized Robertson-Walker spacetimes with a q…

Study properties of bi-warped product submanifolds in specific geometric spaces.

The paper studies conformal Ricci solitons in warped product spaces.

The paper examines conditions for compactness in sequences of warped product length spaces.

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.

Study finds conditions for certain warped product manifolds to be quasi-Einstein.

We prove an almost splitting theorem for the warped product space with warped function $f(r)=\cosh\left(r\sqrt{\fracλ{n-2}}\right)$.

The present article provides a study of $2-$Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a $2-$Killing vector field on a warped product manifold to be parallel are obtained. Moreover, …

In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold. Moreover, we obtain some geometric inequalities for C-totally real doubly warped product submanifolds of generaliz…

Study on Einstein warped spaces with specific connections and curvature properties.

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the Riemann curvature tensor of the ambient manifold. Applying this general theory, we obtain basic inequa…

Geometrically describes surfaces with parallel mean curvature in warped product spaces.

Survey on warped products and their curvature properties.

Warped product construction for Finsler manifolds with curvature conditions.

In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic and Golden Riemannian manifolds. Also, we provide some examples of warped product…

Synthetic proof shows globally hyperbolic Lorentzian spaces with specific curvature are warped products.

B.-Y. Chen initiated the study of warped product submanifolds in his fundamental seminal papers \cite{C1,C2,C2.1}. In this paper, we study contact CR-warped product submanifolds of cosymplectic space forms and prove an optimal inequality by using Gauss and Codazzi equations. In addition, we obtain two geometric inequal…

In this paper, we investigate the null (light-like) sectional curvatures of Lorentzian warped product manifolds. We derive the formulas for the null sectional curvature of many well-known warped product space-time models such as multiply generalized Robertson-Walker space-times, generalized Kasner spacetimes and standa…

The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal…

Study classifies Einstein spaces and warped products in weighted geometry.

New rigidity results for warped product domains.

Study properties of specific submanifolds in metallic Riemannian spaces.

In this article, we present a complete study of two disjoint classes of conformal vector fields on doubly warped product manifolds as well as on doubly warped space-times. Then we study Ricci solitons on doubly warped product manifollds admitting these types of conformal vector fields.

Study on Ricci-Bourguignon solitons on specific product spaces.

The paper examines stability of Minkowski inequalities in warped product spaces.

This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product …

We introduce a notion of doubly warped product of weighted graphs that is consistent with the doubly warped product in the Riemannian setting. We establish various discrete Bakry-Émery Ricci curvature-dimension bounds for such warped products in terms of the curvature of the constituent graphs. This requires deliberate…

Study geometric properties and spectral estimates on warped products.

In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein's equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. …

In this article, we continue the work in \cite{GL} and study a normalized hypersurface flow in the more general ambient setting of warped product spaces. This flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. As an application, the i…

Stability results for geometric equations in warped product spaces.

New findings extend rigidity results to broader classes of manifolds.

Classifies smooth metric measure spaces with two weighted Einstein representatives.