arXiv research

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

Adapted metrics found on complex manifolds.

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

Locally conformally product Lie algebras are characterized and constructed.

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.

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

No conformal product structures on compact manifolds with constant curvature.

We will consider locally conformally balanced manifolds. We prove that a locally conformally balanced condition is not stable under a small deformation. We prove that locally conformally balanced condition is stable under any proper modification. We prove that symmetric products of the Kodaira surface can be resolve to…

In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension $n\geq 3$ is locally a warped product with $(n-1)$-dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons.

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…

Study conformal product structures on reducible Riemannian manifolds.

Electrostatic systems with specific tensors are locally conformally flat.

Locally conformally product structures defined on compact manifolds.

New examples of weakly Einstein conformal products are constructed.

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…

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…

We show that any locally conformally flat ancient solution to the Ricci flow must be rotationally symmetric. As a by-product, we prove that any locally conformally flat Ricci soliton is a gradient soliton in the shrinking and steady cases as well as in the expanding case, provided the soliton has nonnegative curvature.

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

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…

Study on balanced Hermitian structures on Lie algebras twisted by representations.

This is a survey article on the existence of locally conformally flat(LCF) and self-dual(SD) metrics on various basic 4-manifolds like simply-connected ones or product types

Conformal vector fields on LCP manifolds are orthogonal and Killing.

It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson-Walker warped product, if the gradient of the potential function is non null, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily stead…

We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold $Σ_g\timesΣ_h$ does not admit any locally conformally flat metric arising from discrete and faithful representations for $g\geq 2$ and $h\geq 1$

Complex structures found on product of Sasakian manifolds.

Classifies smooth metric measure spaces with two weighted Einstein representatives.

Products of LCK manifolds do not admit LCK structures.

Localized signal representation on graph bundles using Fourier analysis.

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…

Constructs symplectic structures on product manifolds from LCS structures.

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…

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

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella classification admitting a parallel vector field and show that (under some regulari…

We present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not admit locally conformal Kähler metrics and all the structures come from left-invariant locally conformal symplectic structures on the correspon…

This paper describes the characteristic group of LCP structures and their construction.

The paper explores properties of conformal vector fields on almost Kenmotsu manifolds.

We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to characterizing incomplete, simply-connected, Riemannian manifolds with reducible holonomy group whose quotient by a group of homotheties is clo…

We study the problem posed by F. Burstall of developing a theory of isothermic Euclidean submanifolds of dimension greater than or equal to three. As a natural extension of the definition in the surface case, we call a Euclidean submanifold {\it isothermic} if it is locally the image of a conformal immersion of a Riema…

As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions fr…

We show that complete conformally flat manifolds of dimension n>2 with nonnegative Ricci curvature enjoy nice rigidity properties: they are either flat, or locally isometric to a product of a sphere and a line, or are globally conformally equivalent to flat space or to a spherical spaceform. This extends previous works…

Generalizes warped product submersion to conformal case.

We describe the local structure of self-dual gradient Ricci solitons in neutral signature. If the Ricci soliton is non-isotropic then it is locally conformally flat and locally isometric to a warped product of the form $I\times_\varphi N(c)$, where $N(c)$ is a space of constant curvature. If the Ricci soliton is isotro…

The paper studies conformal Ricci solitons in warped product spaces.

A locally conformally Kähler (LCK) manifold is a complex manifold covered by a Kähler manifold, with the covering group acting by homotheties. We show that if such a compact manifold X admits a holomorphic submersion with positive dimensional fibers at least one of which is of Kähler type, then X is globally conformall…

Einstein metrics on products are shown to be warped.

Proves properties of 4-manifolds with scalar curvature constraints.

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non homothetic solutions of the Yamabe problem. Using local rigi…

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