arXiv research

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

Characterizes and examines gradient solitons on doubly warped product manifolds.

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 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.

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 curvatures of doubly warped product Finsler manifold and its components, and consi…

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…

Characterizes certain Kähler manifolds with doubly-warped product structures.

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…

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds $B$ and $F$ into the doubly warped product $_{f}B\times_{b}F$ can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections $_{f}B\times_{b}…

The paper examines gradient ρ-Einstein solitons on specific manifolds and spacetimes.

The paper confirms a conjecture about manifolds with positive curvature.

Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product cont…

We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly warped product up to a zero measure subset formed by an union of leaves. We also…

A. Gray presented an interesting $O\left( n\right)$ invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what con…

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

In this paper, we consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian…

For any manifold $N^p$ admitting an Einstein metric with positive Einstein constant, we study the behavior of the Ricci flow on high-dimensional products $M = N^p \times S^{q+1}$ with doubly-warped product metrics. In particular, we provide a rigorous construction of local, type II, conical singularity formation on suc…

Existence proved for Ricci curvature on sphere product.

Rigidity results for hypersurfaces in warped spacetimes.

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…

Study spherical doubly warped spacetimes for stellar collapse and cosmology.

The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.

Characterizes a specific type of spacetime using vector fields.

Study properties of hyperbolic Yamabe solitons in submanifolds.

Characterizes spacetimes using doubly torqued vectors.

Computer-assisted method finds new Einstein metrics on spheres.

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension $d$ for all $d\geq 4$. These examples result from applying CAT$(0)$/CAT$(-1)$ filling constructions (based on singular doubly warped products) to finite volume hyperbolic manifolds with toral cusps. The groups obtained have a…

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.

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

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.