On the Markus conjecture in convex case

Annals of Global Analysis and Geometry - In this paper, we show that any convex affine domain with a nonempty limit set on the boundary under the action of the identity component of the...     

The geometry of SO(n)\SO0(n, 1)

Consider the Lie group SO₀(n, 1) with the left-invariant metric coming from the Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group acts from the left and right. This paper studies the geometry of the quotient space of the homogeneous submersion SO₀(n, 1) → SO(n)\SO₀(n, 1). It is a cohomogeneity one manifold, which can be expressed as a warped product. Its group of isometries, geodesics, and sectional curvatures are calculated.     

Convex affine domains and Markus conjecture

In this paper we show that any properly convex quasi-homogeneous affine domain with irreducible projective automorphism group is projectively equivalent to a homogeneous affine domain. Then as an application we answer positively the Markus conjecture when the manifold M is in a certain class of convex affine manifolds.Mathematics Subject Classification (1991): 51M10, 57S25This work was supported by Korea Research Foundation Grant (KRF-2002-070-C00010).in final form: 6 October 2003