Two-root Riemannian Manifolds
Differential Geometry
2023-01-27 v4
Abstract
Osserman manifolds are a generalization of locally two-point homogeneous spaces. We introduce -root manifolds in which the reduced Jacobi operator has exactly eigenvalues. We investigate one-root and two-root manifolds as another generalization of locally two-point homogeneous spaces. We prove that there is no two-root Riemannian manifold of odd dimension. In twice an odd dimension, we describe all two-root Riemannian algebraic curvature tensors and give additional conditions for two-root Riemannian manifolds.
Cite
@article{arxiv.2009.12834,
title = {Two-root Riemannian Manifolds},
author = {Vladica Andrejić},
journal= {arXiv preprint arXiv:2009.12834},
year = {2023}
}