arXiv research

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

We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped product type. Our main result is an upper bound on the resonance counting function with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends.

Study finds solutions for complex problems on non-compact manifolds.

Non-existence of warped product semi-slant submanifolds of Kaehler manifolds was proved in [17], it is interesting to find their existence. In this paper, we prove the existence of warped product semi-slant submanifolds of nearly Kaehler manifolds by a characterization. To this end we obtain an inequality for the squar…

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…

New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra …

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.

In this paper we study Inverse Mean Curvature Flow (IMCF) on manifolds that are conformal to a warped product manifold. To this end, we show how the gradient conformal vector field in warped product manifolds is related to the conformal vector field on the conformal metric and use this to gain control of the flow in or…

We prove the existence of Ricci flow starting from a class of metrics with unbounded curvature, which are doubly-warped products over an interval with a spherical factor pinched off at an end. These provide a forward evolution from some known and conjectured finite-time local singularities of Ricci flow, generalizing p…

In this paper, we prove that there are no proper $CRS$ bi-warped product submanifolds other than contact CR-biwarped products in Sasakian manifolds. On the other hand, we prove that if $M$ is a $CRS$ bi-warped product of the form $M=N_T \times_{f_1}N^{n_{1}}_\perp\times_{f_2} N^{n_{2}}_θ$ in a cosymplectic manifold $\w…

Motivated by a recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with the real line admits a complete metric of bounded negative sectional curvature which is an exponentially warped near one end and has finite volume near the othe…

Sharp estimates for p-capacity on manifolds with Ricci curvature bounds.

The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.

Generalizes warped product submersion to conformal case.

The paper explores geometric properties of Riemannian warped product maps and their curvature.

Study on warped product Yamabe solitons with constant fiber curvature.

The paper explores warped-like product metrics with exceptional holonomy groups.

Warped product affects divergences in information geometry.

The paper extends affine connection results to singular warped and twisted products.

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 $N_1$. Warped products play very important roles in differential geometry as well as in physic…

The paper proves rigidity for submanifolds in warped product manifolds.

Paper defines and studies Clairaut warped product Riemannian maps.

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

Study shows how certain metrics can be split into warped products.

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

Characterizes and examines gradient solitons on doubly warped product manifolds.

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

In this paper we study fundamental geometric properties of doubly warped product immersion which is an extension of warped product immersion. Moreover, we study geometric inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds.

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…

The paper studies affine connections on singular warped products and their curvature.

In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is n…

Study investigates concircular curvature on warped products.

In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show tha…

Study Einstein warped products with Einstein base and fiber.

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…

Paper defines new submanifolds in Kaehler manifolds.

New rigidity found for 3D warped product domains.

The paper studies conformal Ricci solitons in warped product spaces.

Study new warped metrics with vanishing Douglas curvature.

Estimates heights of special surfaces in warped products.

The paper studies geometric properties of a specific type of submanifolds in Kaehler manifolds.

Einstein metrics on products are shown to be warped.

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 …

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 notion of warped product manifolds is one of the most fruitful generalizations of R…

Conditions for flat 3-manifolds with diagonal metrics are identified.

New rigidity results for warped product domains.

Backward propagation rules for warped products under Ricci flow.

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…