2007/01/03 by Maria Ivanova, M. S. Ivanova, V. Videv +6 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C20
paper · pdf · doi:10.48550/arxiv.math/0701090
10 pages
arxiv created 2007/02/26 · arxiv updated 2009/12/01
We consider four-dimensional Riemannian manifolds with commuting higher order Jacobi operators defined on two-dimensional orthogonal subspaces (polygons) and on their orthogonal subspaces. More precisely, we discuss higher order Jacobi operator J(X) and its commuting associated operator J(X⊥) induced by the orthogonal complement X⊥ of the vector X, i. e. J(X)\circJ(X⊥)=J(X⊥)∘ J(X). At the end some new central theorems have been cited. The latter are due to P. Gilkey, E. Puffini and V. Videv, and have been recently obtained.