Tori whose covering spaces have convex distance functions

Properties of Distance Functions on Convex Surfaces and Alexandrov Spaces

If X is a convex surface in a Euclidean space, then the squared (intrinsic) distance function dist(x, y) is d.c. (DC, delta-convex) on X×X in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of dist(x, y) on X × X if X is an Alexandrov space with nonnegative curvature. Applications concerning r-boundaries (distance spheres) and the ambiguous locus (ex...

Ahler Manifolds Whose Universal Covering Spaces Are Biholomorphic

These manifolds M are complex tori up to nite etale coverings, or satisfy both inequalities (M) < n 3 and q(M) < n 3.

Curvature homogeneous spaces whose curvature tensors have large symmetries

We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large” Lie subalgebras h of so(n). In this paper we deal with the cases of h = so(r)⊕ so(n− r) (2 ≤ r ≤ n− r), so(n− 2), and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.

On Non-smooth Convex Distance Functions

Harmonic functions in non-locally convex spaces