arXiv research

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…

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

In this paper, we define a semi-symmetric metric Killing vector field, then study semi-symmetric metric Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection. We also study Killing and 2-Killing vector fields on multiply warped products.

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

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…

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…

Study on four-dimensional Ricci solitons and multiply warped Ricci flow solutions.

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…

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

The paper studies Einstein hypersurfaces in a specific warped product space.

We prove some isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We then relate them to inequalities involving the higher order mean-curvature integrals. We also apply our results to obtain sharp eigenvalue estimates and some sharp geometric inequalities i…

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…

Backward propagation rules for warped products under Ricci flow.

Study proves rigidity of certain gradient steady Ricci solitons with harmonic Weyl curvature.

By applying an average method in PDE, we obtain a dichotomy between "constancy" and "infinity" of the warping functions on complete noncompact Riemannian manifolds for an appropriate isometric immersion of a multiply warped product manifold $N_1\times_{f_2} N_2 \times \cdots \times _{f_k} N_k\,$ into a Riemannian mani…

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

We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in Kähler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a non-trivial biwarped product submanifold of a certain type by giving an illustrate example. …

Study properties of hyperbolic Yamabe solitons in submanifolds.

We study a multiply warped products manifold associated with the Reissner-Nordstrom metric to investigate the physical properties inside the black hole event horizons. It is shown that, different from the uncharged Schwarzschild metric, the Ricci curvature components inside the Reissner-Nordstrom black hole horizons ar…

Study classifies gradient almost Ricci solitons with harmonic Weyl tensor.

The paper studies Einstein-Hilbert action on complex manifolds.

The paper explores formulas and applications for mixed scalar curvature in multi-product manifolds.

The paper proves integral formulas for manifolds with multiple orthogonal distributions.

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.

Warped product affects divergences in information geometry.

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…

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…

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.

Paper defines new submanifolds in Kaehler manifolds.

New rigidity found for 3D warped product domains.

For a closed, connected direct product Riemannian manifold $(M, g)=(M_1\times\cdots\times M_l, g_1\oplus\cdots\oplus g_l)$, we define its multiconformal class $[\![ g ]\!]$ as the totality $\{f_1^2g_1\oplus \cdots\oplus f_l^2g_l\}$ of all Riemannian metrics obtained from multiplying the metric $g_i$ of each factor $M_…

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.