Displaying similar documents to “Metrics in the sphere of a C*-module”

Metrics in the set of partial isometries with finite rank

Esteban Andruchow, Gustavo Corach (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let I be the set of partial isometries with finite rank of an infinite dimensional Hilbert space H . We show that I is a smooth submanifold of the Hilbert space B 2 H of Hilbert-Schmidt operators of H and that each connected component is the set I N , which consists of all partial isometries of rank N < . Furthermore, I is a homogeneous space of U × U , where U is the classical Banach-Lie group of unitary operators of H , which are Hilbert-Schmidt perturbations of the identity. We introduce two Riemannian...

The Hilbert Scheme of Buchsbaum space curves

Jan O. Kleppe (2012)

Annales de l’institut Fourier

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We consider the Hilbert scheme H ( d , g ) of space curves C with homogeneous ideal I ( C ) : = H * 0 ( C ) and Rao module M : = H * 1 ( C ) . By taking suitable generizations (deformations to a more general curve) C of C , we simplify the minimal free resolution of I ( C ) by e.g making consecutive free summands (ghost-terms) disappear in a free resolution of I ( C ) . Using this for Buchsbaum curves of diameter one ( M v 0 for only one v ), we establish a one-to-one correspondence between the set 𝒮 of irreducible components of H ( d , g ) that contain ( C ) and a...

Timelike B 2 -slant helices in Minkowski space E 1 4

Ahmad T. Ali, Rafael López (2010)

Archivum Mathematicum

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We consider a unit speed timelike curve α in Minkowski 4-space 𝐄 1 4 and denote the Frenet frame of α by { 𝐓 , 𝐍 , 𝐁 1 , 𝐁 2 } . We say that α is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction U of 𝐄 1 4 . In this work we study those helices where the function 𝐁 2 , U is constant and we give different characterizations of such curves.

On sprays and connections

Kozma, László

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[For the entire collection see Zbl 0699.00032.] A connection structure (M,H) and a path structure (M,S) on the manifold M are called compatible, if S ( v ) = H ( v , v ) , v T M , locally G i ( x , y ) = y j Γ j i ( x , y ) , where G i and Γ j i express the semi-spray S and the connection map H, resp. In the linear case of H its geodesic spray S is quadratic: G i ( x , y ) = Γ j k i ( k ) y j y k . On the contrary, the homogeneity condition of S induces the relation for the compatible connection H, y j ( Γ j i μ t ) = t y j Γ j i , whence it follows not that H is linear, i.e. if a connection structure is compatible with a...