Some Properties of the Curvature Operator of a Riemannian Manifold.
The first part of this paper is concerned with geometrical and cohomological properties of Lie flows on compact manifolds. Relations between these properties and the Euler class of the flow are given.The second part deals with 3-codimensional Lie flows. Using the classification of 3-dimensional Lie algebras we give cohomological obstructions for a compact manifold admits a Lie flow transversely modeled on a given Lie algebra.
Nearly-quaternionic Kähler manifolds of dimension at least are shown to be quaternionic Kähler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic Kähler are also found.
In this note, we are concerned with the Kozlowski-Simon conjecture on ovaloids and prove that it is correct under additional conditions.
We obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold.