arXiv research

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

Paper defines and studies Clairaut warped product Riemannian maps.

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

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

Study conformal product structures on reducible Riemannian manifolds.

Study on Riemannian Poisson warped product spaces and their properties.

The study characterizes submanifolds in product spaces.

Study on properties of tangential hypersurfaces in product-like manifolds.

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

Researchers solve a Riemannian geometry problem using warped products.

The study examines minimal surfaces in Riemannian products of surfaces.

Study adds scalar curvatures of mapped manifolds to Riemannian products.

Study properties of specific submanifolds in metallic Riemannian spaces.

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

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…

Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metric and the product structure.

The paper characterizes biharmonic submersions from product manifolds.

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 main aim of the present work is to obtain some curvature properties of the manifolds from two classes of Riemannian product manifolds. These classes are two basic classes from Naveira classification of Riemannian almost product manifolds.

The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an…

Study relationships between intrinsic and extrinsic invariants of Riemannian almost k-product 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 …

A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable structure is obtained, and in the second case - a pseudo-Riemannian one. Each belo…

Study on 3D manifolds with specific tensor structures and their properties.

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…

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…

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…

In the present work, we introduce a linear connection (preserving the almost product structure and the Riemannian metric) on Riemannian almost product manifolds. This connection, called P-connection, is an analogue of the first canonical connection of Lichnerowicz in the Hermitian geometry and the B-connection in the g…

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

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 …

We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the Dirac operator on compact Riemannian spin manifolds with locally product structures. We also provide some examples (limiting manifolds) for t…

Warped product construction for Finsler manifolds with curvature conditions.

Maps are shown to be Riemannian products with Ricci-flat fibers.

In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact manifolds.

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

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

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

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

We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We…

We study twistor forms on products of compact Riemannian manifolds and show that they are defined by Killing forms on the factors. The main result of this note is a necessary step in the classification of compact Riemannian manifolds with non-generic holonomy carrying twistor forms.

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 class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.

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…

The study proves a theorem on Riemannian manifolds for wedge products of weakly convergent differential forms.

A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, is considered. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant, and it acts as an isometry with respect to the metric. The Riemannian product manifold a…

Study Einstein warped products with Einstein base and fiber.

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

Proves Riemannian starshape of capacitary potential levels.