We consider pure spinor strings that propagate in the background generated by a sequence of TsT transformations. We use the fact that U(1) isometry variables of TsT-transformed background are related to the isometry variables of the initial background in the universal way that is independent of the details of the background. We will argue that after redefinitions of pure spinors and the fermion...

A factor graph of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that the d-dimensional Poisson process has a one-ended tree as a factor graph. This implies that the Poisson points can be given an ordering isomorphic to the usual ordering of the integers in a deterministic iso...

In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also reciprocal of potential function subharmonic, then manifold isometric to Euclidean sphere. As consequence, showed four dimensional satisfying some conditions $\mathbb{S}^4$ $\mathbb{RP}^4$ $\mathbb{CP}^2$. We deduced ...

Given a 2-manifold, fundamental question to ask is which groups can be realized as the isometry group of Riemannian metric constant curvature on manifold. In this paper, we give nearly complete classification such for infinite-genus 2-manifolds with no planar ends. Surprisingly, show there an uncountable class where every countable (namely, those self-similar end spaces). We apply result obtain...

We show that if T is an isometry (as metric spaces) from an open subgroup of the invertible group A of a unital Banach algebra A onto an open subgroup of the invertible group B of a unital Banach algebra B, then T is extended to a real-linear isometry up to translation between these Banach algebras. We consider multiplicativity or unti-multiplicativity of the isometry. Note that a unital linear...

Let M(n) denote the group of orientation-preserving isometries of H. Classically, one uses the disk model for H to define the dynamical type of an isometry. In this model an isometry is elliptic if it has a fixed point on the disk. An isometry is parabolic, resp. hyperbolic, if it is not elliptic and has one, resp. two fixed points on the conformal boundary of the hyperbolic space. If in additi...

Despite the promise of low-dimensional manifold models for image processing, computer vision, and machine learning tasks, their utility has been hamstrung in practice by two fundamental challenges. First, practical image manifolds are non-isometric to their underlying parameter space, while the state-of-the-art manifold modeling and learning frameworks assume isometry. Second, practical image m...

Abstract We give necessary and sufficient conditions on an m -isometry to have invertible -isometrical extension. As particular cases, we a useful characterization for general unilateral weighted shift $$\ell $$ ℓ -Jordan isometries. In particular, every isometry operator has $$(2\ell -1)$$ <mml:mo...

It was pointed out by Couch and Torrence that the extreme Reissner-Nordström solution possesses a discrete conformal isometry. Using results of Romans, it is shown that such a symmetry also exists when a non-zero cosmological constant is allowed. Introduction In [1], Couch and Torrence found a conformal isometry that interchanges the event horizon and null infinity J of an extremal Reissner-Nor...