Related papers: Conformal vector fields on doubly warped product m…
In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…
We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them…
We consider a problem of prescribing the partial Ricci curvature on a locally conformally flat manifold $(M^n, g)$ endowed with the complementary orthogonal distributions $D_1$ and $D_2$. We provide conditions for symmetric $(0,2)$-tensors…
We give characterizations of affine transformations and affine vector fields in terms of the spray. By utilizing the Jacobi type equation that characterizes affine vector fields, we prove some rigidity theorems of affine vector fields on…
We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics.…
We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show…
Robertson-Walker and Generalized Robertson-Walker spacetimes may be characterized by the existence of a time-like unit torse-forming vector field, with other constrains. We show that Twisted manifolds may still be characterized by the…
In this note, I discuss in some detail the dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in math.AG/0402015, and used in math.QA/0412149 to…
In this article, we investigate global norm of potential vector field in Ricci soliton. In particular, we have deduced certain conditions so that the potential vector field has finite global norm in expanding Ricci soliton. We have also…
In this paper, we study structures of almost Yamabe solitons which are not necessarily gradient. First, we investigate conditions that both compact and noncompact almost Yamabe solitons become trivial solitons which means the given vector…
In this paper we study in details the properties of the duality product of multivectors and multiforms (used in the definition of the hyperbolic Clifford algebra of multivefors) and introduce the theory of the k multivector and l multiform…
We prove that there exists a gradient expanding Ricci soliton asymptotic to any given cone over the product of a round sphere and a Ricci flat manifold. In particular we obtain asymptotically conical expanding Ricci solitons with positive…
In this note we characterize 1+n doubly twisted spacetimes in terms of `doubly torqued' vector fields. They extend Bang-Yen Chen's characterization of twisted and generalized Robertson-Walker spacetimes with torqued and concircular vector…
We study two-color surface solitons in two-dimensional photonic lattices with quadratic nonlinear response. We demonstrate that such parametrically coupled optical localized modes can exist in the corners or at the edges of a square…
We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and…
In this paper, we prove that expanding gradient Ricci solitons with (positively) pinched Ricci curvature are trivial ones. Namely, they are either compact or flat.
In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field \xi are discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field \xi are determined. Conditions for the Ricci soliton…
We obtain a Shimorin-Wold-type decomposition for a doubly commuting covariant representation of a product system of $C^*$-correspondences. This extends a recent Wold-type decomposition by Jeu and Pinto for a $q$-doubly commuting isometries.…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
We apply Kadanoff's theory of marginal deformations of conformal field theories to twistfield deformations of Z_2 orbifold models in K3 moduli space. These deformations lead away from the Z_2 orbifold sub-moduli-space and hence help to…