2014/03/07 by Peter Gilkey, Gilkey, Peter, Bronson Lim +1
Mathematics · Physics and Astronomy · #53A15 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53A15
paper · pdf · doi:10.48550/arxiv.1403.1900
arxiv created 2014/03/07 · openalex publication_date 2014/03/07 · arxiv updated 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A curvature model (V,A) is a real vector space V which is equipped with a "curvature operator" A(x,y)z that A has the same symmetries as an affine curvature operator; A(x,y)z=-A(y,x)z and A(x,y)z+A(y,z)x+A(z,x)y=0. Such a model is called projective affine Osserman if the spectrum of the Jacobi operator J(y):x->A(x,y)y, is projectively constant. There are topological conditions imposed on such a model by Adam's Theorem concerning vector fields on spheres. In this paper we construct projective affine Osserman curvature models when the dimension is odd, when the dimension is congruent to 2 mod 4, and when the dimension is congruent to 4 mod 8 for all the eigenvalue structure is allowed by Adam's Theorem.