Article

On the holonomy algebra of manifolds with pure curvature operator

"We study the holonomy algebra of Riemannian manifolds with pure curvature operator. We conclude that locally irreducible K¨ahler manifolds of dimension greater than four do not have pure curvature operator. A similar result is obtained for compact locally irreducible K¨ahler four-manifolds of nonnegative scalar curvature. We also study compact Riemannian manifolds with pure curvature operator and some special curvature conditions."

Relationships

Items