arXiv research

Generalizes warped product submersion to conformal case.

The paper studies conformal Ricci solitons in warped product spaces.

Einstein metrics on products are shown to be warped.

Constructing a conformal product structure on $S^3$ using the Reeb foliation.

Study describes conformal product structures on compact Kähler manifolds.

Study conformal product structures on reducible Riemannian manifolds.

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…

No conformal product structures on compact manifolds with constant curvature.

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

Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to investigate the holonomy of the a…

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

Paper proves existence of PMC hypersurfaces in conformal 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.

New result on Einstein manifolds using conformal product structures.

In this short note, we prove that conformal classes which are small perturbations of a product conformal class on a product with a standard sphere admit a metric extremal for some Laplace eigenvalue. As part of the arguments we obtain perturbed harmonic maps with constant density.

Study properties of bi-warped product submanifolds in specific geometric spaces.

The paper studies geometric properties of a specific type of submanifolds in Kaehler manifolds.

Adapted metrics found on complex manifolds.

Locally conformally product Lie algebras are characterized and constructed.

New examples of weakly Einstein conformal products are constructed.

In this paper we study Inverse Mean Curvature Flow (IMCF) on manifolds that are conformal to a warped product manifold. To this end, we show how the gradient conformal vector field in warped product manifolds is related to the conformal vector field on the conformal metric and use this to gain control of the flow in or…

We introduce the concept of a base conformal warped product of two pseudo-Riemannian manifolds. We also define a subclass of this structure called as a special base conformal warped product. After, we explicitly mention many of the relevant fields where metrics of these forms and also considerations about their curvatu…

We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where the conformal factor depends on both manifolds simultaneously. If both factors ar…

Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conforma…

New method proves mateability of triangle groups with Blaschke products.

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature…

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.

Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h).

Study on Ricci-Bourguignon solitons on specific product spaces.

We discuss conformal deformation and warped products on some open manifolds. We discuss how these can be applied to construct Riemannian metrics with specific scalar curvature functions.

Study LCP structures on solvmanifolds, complete list up to 5 dimensions.

Classifies smooth metric measure spaces with two weighted Einstein representatives.

In this paper, we investigate the condition on warped product manifold of a Kenmotsu manifold and the real line to be a conformal Kahler manifold. This result demonstrates the close relation of Kenmotsu and Kahler manifolds.

We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping funct…

Note proves a mathematical invariant can be close to a sphere's.

Locally conformally product structures defined on compact manifolds.

We proved that a conformal immersion of $M_0^{n_0}\times M_1^{n_1}$ as an hipersurface in a Euclidean space must be an extrinsic product of immersions, under the assumption that $n_0, n_1 \geq 2$ and that $M^{n_0}_0\times M^{n_1}_1$ is not conformally flat. We also stated a similar theorem for an arbitrary number of fa…

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.} \textbf{21}, 2153-2177 and some of their basic proper…

Study on special warped product manifolds with Einstein metrics.

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

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

The study improves Wintgen inequalities for submanifolds in specific geometric spaces.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

n this paper, we obtain a geometric inequality between the length of the second fundamental form and the length of Lee form in terms of the warping function for a CR-warped product submanifold in a locally conformal Kaehler space form. The equality case is also investigated. Furthermore, the inequality is discussed for…

The abstract manifold cannot have uniformly quasiregular self-maps.

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

Electrostatic systems with specific tensors are locally conformally flat.

In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is conformal to an n-dimensional pseudo-Euclidean space invariant under the action…