arXiv research

Study on Riemannian Poisson warped product spaces and their properties.

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

Study properties of specific submanifolds in metallic Riemannian spaces.

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

The paper classifies product minimal Lagrangian submanifolds in complex space forms.

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem…

The study examines minimal surfaces in Riemannian products of surfaces.

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

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 …

The study characterizes submanifolds in product spaces.

The study restricts stable minimal immersions in product spaces to specific configurations.

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…

Survey on warped products and their curvature properties.

Classifies vacuum static spaces with harmonic curvature.

We show that a simply connected Riemannian homogeneous space M which admits a totally geodesic hypersurface F is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped product of the Euclidean space and a homogeneous space, or (c) the twisted product o…

Researchers solve a Riemannian geometry problem using warped products.

Study of complex structures on product twistor spaces for 4D manifolds.

We give some fundamental properties of the induced structures on submanifolds immersed in almost product or locally product Riemannian manifolds. We study the induced structure by the composition of two isometric immersions on submanifolds in an almost product Riemannian manifold. We give an effective construction for …

Defines semi-symmetric metric connection on super warped products.

The study finds complete translating solitons for certain powers of Gaussian curvature in Riemannian products.

The paper derives optimal inequalities for bi-slant submanifolds in metallic Riemannian space forms.

Study Einstein warped products with Einstein base and fiber.

Linear classifiers in product space forms improve scRNA-seq data classification.

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

Non-trivial examples of Riemannian almost product structures are constructed on the product bundle of the positive and negative twistor spaces of an oriented Riemannian four-manifold. The Gil-Medrano and Naveira types of these structures are determined and a geometric interpretation of the corresponding classes is give…

Warped product construction for Finsler manifolds with curvature conditions.

Necessary and sufficient conditions for a Riemannian product to be conformally equivalent to an Einstein manifold are given. Such spaces which are complete are characterized.

The paper proves a new inequality for submanifolds in Riemannian space forms and applies it to find minimal submanifolds.

The paper characterizes biharmonic submersions from product manifolds.

Characterizes warping functions in Einstein Poisson warped spaces.

Study on surfaces in product space with curvature inequality.

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold endowed with a polar metric. For a product manifold endowed with a polar metric, our …

Formula for spacelike submanifolds in warped products.

The study extends Hano's theorem to semi-Riemannian product manifolds with specific conditions.

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

In this paper, we prove a classification theorem for the stable compact minimal submanifolds of the Riemannian product of an $m_1$-dimensional ($m_1\geq3$) hypersurface $M_1$ in the Euclidean space and any Riemannian manifold $M_2$, when the sectional curvature $K_{M_1}$ of $M_1$ satisfies $\frac{1}{\sqrt{m_1-1}}\leq K…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i…

We show the Chas-Sullivan product (on the homology of the free loop space of a Riemannian manifold) is related to the Morse index of its closed geodesics. We construct related products in the cohomology of the free loop space and of the based loop space, and show they are nontrivial.

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

Study characterizes Einstein metrics in warped product spaces.

The study classifies parallel mean curvature spheres in a sphere-hyperbolic product space.

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

Proves curvature comparison for Riemannian bands in low dimensions.

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 curvature tensor and the scalar curvature are computed in the space of positive definite real matrices endowed by the Kubo-Mori inner product as a Riemannian metric.

We classify Riemannian surfaces admitting associated families in three dimensional homogeneous spaces with four-dimensional isometry groups and in a wide family of (semi-Riemannian) warped products, with an extra natural condition (namely, rotating structure vector field). We prove that, provided the surface is not tot…

Characterizes higher rank model geometries using antipodal sets.

The paper studies conformal Ricci solitons in warped product spaces.