On the Orbit Structures of SU (n)-Actions on Manifolds of the Type of Euclidean, Spherical or Projective Spaces.
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...
In this paper we describe the orbit structure of -actions of on the solid torus having and as the only compact orbits, and as singular set.
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...
Let be a compact lie group. We introduce the set for every smooth manifold . It consists of equivalence classes of pair where is a map which defines a homotopy equivalence from to . Two pairs , for , are equivalent if there is a homotopy equivalence such that is homotopic to .Properties of the set and related to the representation of on the tangent spaces of and at the fixed points. For the case and is the manifold defined by a “linear” action on complex...