Related papers: Conformal vector fields on doubly warped product m…

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…

We investigate second order conformal perturbation theory for $\mathbb{Z}_2$ orbifolds of conformal field theories in two dimensions. To evaluate the necessary twisted sector correlation functions and their integrals, we map them from the…

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in $S^4$, are studied in this paper. We define two kinds of transforms for such a…

We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped…

Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber preserving vector fields on TM have well-known physical interpretations and have been studied by physicists and geometricians. Here we define a…

We introduce a full set of rules to directly express all $M$-point conformal blocks in one- and two-dimensional conformal field theories, irrespective of the topology. The $M$-point conformal blocks are power series expansion in some…

We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…

A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…

We report on the first experimental observation of a novel type of optical vector soliton, a {\em dipole-mode soliton}, recently predicted theoretically. We show that these vector solitons can be generated in a photorefractive medium…

In this paper, we begin by introducing Clairaut Riemannian warped product maps and establish the condition under which a regular curve becomes a geodesic. We obtain the conditions for a Riemannian warped product map to be Clairaut…

In this paper, we study solitons on $3$-dimensional manifolds. In particular, we show that $3$-dimensional pseudo-symmetric gradient Ricci solitons and nontrivial gradient Yamabe solitons are locally isometric to either $\mathbb{R}^{3}$,…

We discuss the geometry of warped foliations. After examining the Levi-Civita connection, we describe the formulae for sectional, Ricci and scalar curvatures. In the final part of this note, we present some examples.

We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…

We have investigated mixed-gap vector solitons involving incoherently coupled fundamental and dipole components in a parity-time (PT) symmetric lattice with saturable nonlinearity. For the focusing case, vector solitons emerge from the…

We give a result estimating the dimension of the Lie algebra of Killing vector fields on an irreducible non-trivial gradient Ricci soliton. Then we study the structure of this manifold when the maximal dimension is attained. There are local…

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…

The purpose of this article is to study generalized quasi Yamabe gradient solitons on warped product manifolds. First, we obtain some necessary and sufficient conditions for the existence of generalized quasi Yamabe gradient solitons…

In this paper we consider $M = B\times_{f}F$ warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber $F$ is necessarily Einstein manifold. We provide all such solutions in the…

Given two Riemannian manifolds $(B,g_B)$ and $(F,g_F)$, we give harmonicity conditions for vector fields on the Riemannian warped product $B\times_fF$, with $f:B \longrightarrow ]0,+\infty[$, using a characteristic variational condition.…

This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…