arXiv research

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

Study spherical doubly warped spacetimes for stellar collapse and cosmology.

Characterizes a specific type of spacetime using vector fields.

Characterizes spacetimes using doubly torqued vectors.

Rigidity results for hypersurfaces in warped spacetimes.

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 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 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 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…

Study properties of hyperbolic Yamabe solitons in submanifolds.

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

The paper confirms a conjecture about manifolds with positive curvature.

The paper explores null distance convergence for warped product spacetimes.

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…

Warped-product black hole spacetimes are $C^0$-inextendible.

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…

Study causal structure of warped spacetimes using novel pre-length spaces.

Study constructs non-Riemannian Finsler metrics using warped product.

Paper studies pseudo-projective tensors on warped products.

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…

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. …

Study shows nonextendibility of warped spacelike singularities in specific spacetimes.

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…

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…

The paper studies conformal Ricci solitons in warped product spaces.

In this paper, we deduce some rigidity results in warped product spaces under normal variations of CMC hypersurfaces. In particular, we prove the existence of one-parameter families locally rigid on the spatial fiber of Anti-de Sitter Schwarzschild spacetime and one-parameter families with bifurcation points on the spa…

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…

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…

Study extends null distance concept to Lorentzian length spaces for spacetime analysis.

Study on gradient solitons on specific manifolds.

The Levi-Civita connection and geodesic equations for a stationary spacetime are studied in depth. General formulae which generalize those for warped products are obtained. These results are applicated to some regions of Kerr spacetime previously studied by using variational methods. We show that they are neither space…

Study on spacelike submanifolds in generalized Schwarzschild spacetimes with lightlike foliations.

Study finds conditions for stationary spacelike surfaces in a generalized Robertson-Walker spacetime.

Theorem proves spectral rigidity of warped product metrics.

A generalized Robertson-Walker spacetime is the warped product with base an open interval of the real line endowed with the opposite of its metric and base any Riemannian manifold. The family of generalized Robertson-Walker spacetimes widely extends the one of classical Robertson-Walker spacetimes. In this article we p…

Study translators in Generalised Robertson-Walker spacetimes, identifying warping functions and classifying examples.

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 suitable examples of such manifolds. They are quasi-Einstein or not.

In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of spac…

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

Existence proved for Ricci curvature on sphere product.