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Conformally geodesic mappings satisfying a certain initial condition

Hana Chudá, Josef Mikeš (2011)

Archivum Mathematicum

In this paper we study conformally geodesic mappings between pseudo-Riemannian manifolds ( M , g ) and ( M ¯ , g ¯ ) , i.e. mappings f : M → M ¯ satisfying f = f 1 ∘ f 2 ∘ f 3 , where f 1 , f 3 are conformal mappings and f 2 is a geodesic mapping. Suppose that the initial condition f * g ¯ = k g is satisfied at a point x 0 ∈ M and that at this point the conformal Weyl tensor does not vanish. We prove that then f is necessarily conformal.

Connessioni adattate ad un Riferimento in Relatività Generale

Giorgio Ferrarese, Donato Bini, Gianluca Gemelli (1994)

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

I vari metodi di definire connessioni adattate ad un Riferimento fisico vengono qui ricondotti ad un unico formalismo. Viene inoltre introdotta la nozione generale di campo gravitazionale affine adattato (sia al Riferimento che alla connessione).

Curvature homogeneity of affine connections on two-dimensional manifolds

Oldřich Kowalski, Barbara Opozda, Zdeněk Vlášek (1999)

Colloquium Mathematicae

Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.

Curvature properties of φ-null Osserman Lorentzian S-manifolds

Letizia Brunetti, Angelo Caldarella (2014)

Open Mathematics

We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds and we use...

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications

In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

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