A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

Within the frame of decision aid literature, decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines. In decision situations with multiple individuals, each one has his own knowledge on the alternatives of the decision problem. The use of information assessed in different domains is not a seldom situation. This no...

This paper introduces a new concept of least community that is as homogeneous as a random graph, and develops a new community detection algorithm from the perspective of homogeneity or heterogeneity. Based on this concept, we adopt head/tail breaks – a newly developed classification scheme for data with a heavy-tailed distribution – and rely on edge betweenness given its heavy-tailed distributi...

We will drop the compactness hypothesis on G in the results of §6, doing this in such a way that problems can be reduced to the compact case. This involves the notions of reductive Lie groups and algebras and Cartan involutions. Let © be a Lie algebra. A subalgebra S c © is called a reductive subaU gebra if the representation ad%\® of ίΐ on © is fully reducible. © is called reductive if it is a...

Considerable recent work on the evolution of behaviour has been set in structured populations. An interesting “cancellation” result is known for structures, such as lattices, cycles and island models, which are homogeneous in the sense that the population “looks the same” from every site. In such populations all proximate or immediate fitness effects on others (for example, payoffs in a game or...