Positive scalar curvature on foliations: The noncompact case

Positive Scalar Curvature

One of the striking initial applications of the Seiberg-Witten invariants was to give new obstructions to the existence of Riemannian metrics of positive scalar curvature on 4– manifolds. The vanishing of the Seiberg–Witten invariants of a manifold admitting such a metric may be viewed as a non-linear generalization of the classic conditions [12, 11] derived from the Dirac operator. If a manifo...

Hyperpolar Homogeneous Foliations on Noncompact Symmetric Spaces

We introduce examples of hyperpolar actions on noncompact symmetric spaces that induce a regular foliation. We study some properties of these actions. Finally, we show that any hyperpolar action on a noncompact symmetric space that induces a regular foliation is one of these examples.

On Complete Noncompact Kähler Manifolds with Positive Bisectional Curvature

We prove that a complete noncompact Kähler manifold Mof positive bisectional curvature satisfying suitable growth conditions is biholomorphic to a pseudoconvex domain of C and we show that the manifold is topologically R2n. In particular, when M is a Kähler surface of positive bisectional curvature satisfying certain natural geometric growth conditions, it is biholomorphic to C2.

Positive Scalar Curvature and Surgery

Foliations and Noncompact Transformation Groups

Introduction. Let G be a Lie group and M a compact C manifold. In [2] Anosov actions of G on M are defined and proved to be structurally stable. In this announcement we are concerned with the foliation ^ of M defined by the orbits of G. Under the assumption that G is connected, # is C stable (3). If G is connected and nilpotent, G has a compact orbit (4). If G is merely solvable, however, there...