2002/05/08 by Peter Gilkey, Gilkey, Peter, Raina Ivanova +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Tensor decomposition and applications #math.DG #msc:53B30
paper · pdf · doi:10.48550/arxiv.math/0205078
arxiv created 2002/05/08 · arxiv updated 2009/11/30
Let M be a pseudo-Riemannian manifold with a pseudo-Hermitian complex structure J. We give necessary and sufficient conditions that the curvature operator R(π) is complex linear when π is a J invariant real 2 plane. Under this assumption, we study when M is complex IP - i.e. the spectrum, or more generally the Jordan normal form, of R(π) is constant on the Grassmannian of complex spacelike or timelike lines. Methods from algebraic topology are used to obtain restrictions on the spectrum of a complex IP algebraic curvature tensor.