arXiv research

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

Paper defines and studies Clairaut warped product Riemannian maps.

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

Study on Riemannian Poisson warped product spaces and their properties.

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…

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…

Researchers solve a Riemannian geometry problem using warped products.

Study Einstein warped products with Einstein base and fiber.

Warped product construction for Finsler manifolds with curvature conditions.

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

Generalizes warped product submersion to conformal case.

Study constructs non-Riemannian Finsler metrics using warped product.

The paper introduces and studies a new type of submersion in Riemannian geometry.

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.

Characterizes warping functions in Einstein Poisson warped spaces.

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

The study characterizes geometries of hypersurfaces in warped product and conformal manifolds.

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Rie…

We characterize the metallic structure on the product of two metallic manifolds in terms of metallic maps and provide a necessary and sufficient condition for the warped product of two locally metallic Riemannian manifolds to be locally metallic. The particular case of product manifolds is discussed and an example of m…

Defines semi-symmetric metric connection on super warped products.

Upper bounds for Steklov eigenvalues of warped products are derived.

Study geometric properties and spectral estimates on warped products.

Survey on warped products and their curvature properties.

The paper characterizes biharmonic submersions from product manifolds.

The paper studies conformal Ricci solitons in warped product spaces.

Proves curvature comparison for Riemannian bands in low dimensions.

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

The paper studies Einstein-type structures in warped product manifolds.

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…

Paper defines new submanifolds in Kaehler manifolds.

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

We introduce warped product skew semi-invariant submanifolds of order $1$ of a locally product Riemannian manifold. We give a necessary and sufficient condition for skew semi-invariant submanifold of order 1 to be a locally warped product. We also prove that the invariant distribution which is involved in the definitio…

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

In this paper, we study some properties of warped product pointwise bi-slant submanifolds in locally metallic Riemannian manifolds and we construct some examples in Euclidean spaces.

In this paper we consider a class of Einstein warped product semi-Riemannian manifolds $\widehat{M} = M^{n}\times_{f}N^{m}$ with $n\geq 3$ and $m\geq 2$. For $\widehat{M}$ with compact base and Ricci-flat fiber, we prove that $\widehat{M}$ is simply a Riemannian product space. Then, when the base $M$ is conformal to a …

In this paper we prove two inequalities relating the warping function to various curvature terms, for warped products isometrically immersed in Riemannian manifolds. This extends work of B. Y. Chen for the case of immersions into space forms. Finally we give an application where the target manifold is the Clifford toru…

The study compares and finds Yamabe constants on warped products.

We present the necessary and sufficient conditions for constructing gradient Ricci almost solitons that are realized as warped products. This will be done by means of Bishop-O'Neill's formulas and a particular study of Riemannian manifolds satisfying a Ricci-Hessian type equation. We prove existence results and give an…

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

Paper shows isotropic $E$- and $S$-curvatures are equivalent in warped Finsler metrics.

Study hot spots on warped product manifolds and infinite cones.

Study characterizes Einstein metrics in warped product spaces.

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…

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…

In this paper we show that an expanding or steady gradient Ricci soliton warped product $B^n\times_f F^m$, $m>1$, whose warping function $f$ reaches both maximum and minimum must be a Riemannian product. Moreover, we present a necessary and sufficient condition for constructing a gradient Ricci soliton warped product. …

Study on special symmetries in biwarped product 3-manifolds.

The paper defines and analyzes curvature tensors on super twisted product spaces.

The special nature of gradient Yamabe soliton equation which was first observed by Cao-Sun-Zhang\cite{CaoSunZhang} shows that a complete gradient Yamabe soliton with non-constant potential function is either defined on the Euclidean space with rotational symmetry, or on the warped product of the real line with a manifo…