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On the topology of spherically symmetric space-times

J. Szenthe (2004)

Open Mathematics

Spherically symmetric space-times have attained considerable attention ever since the early beginnings of the theory of general relativity. In fact, they have appeared already in the papers of K. Schwarzschild [12] and W. De Sitter [5] which were published in 1916 and 1917 respectively soon after Einstein's epoch-making work [7] in 1915. The present survey is concerned mainly with recent results pertainig to the toplogy of spherically symmetric space-times. Definition. By space-time a connected...

Orbit Structure of certain 2 -actions on solid torus

C. Maquera, L. F. Martins (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we describe the orbit structure of   C 2 -actions of   2   on the solid torus   S 1 × D 2   having   S 1 × { 0 }   and   S 1 × D 2   as the only compact orbits, and   S 1 × { 0 }   as singular set.

Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds

Dmitri Alekseevsky, Yoshinobu Kamishima (2004)

Open Mathematics

We define notion of a quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations. We associate with such a structure an Einstein metric on M and establish relations between quaternionic CR structures, contact pseudo-metric 3-structures and pseudo-Sasakian 3-structures. Homogeneous examples of (para)-quaternionic CR manifolds are given and a reduction construction of non...

Real algebraic actions on projective spaces - A survey

Ted Petrie (1973)

Annales de l'institut Fourier

Let G be a compact lie group. We introduce the set S G ( Y ) for every smooth G manifold Y . It consists of equivalence classes of pair ( X , f ) where f : X Y is a G map which defines a homotopy equivalence from X to Y . Two pairs ( X i , f i ) , for i = 0 , 1 , are equivalent if there is a G homotopy equivalence φ : X 0 X 1 such that f 0 is G homotopic to f 1 φ .Properties of the set S G ( Y ) and related to the representation of G on the tangent spaces of X and Y at the fixed points. For the case G = S 1 and Y is the S 1 manifold defined by a “linear” S 1 action on complex...

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