Two-root Riemannian Manifolds

Vladica Andrejić

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arXiv · 2009.12834

Two-root Riemannian Manifolds

Vladica Andrejić

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Abstract

Osserman manifolds are a generalization of locally two-point homogeneous spaces. We introduce $k$-root manifolds in which the reduced Jacobi operator has exactly $k$ 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.

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Vladica Andrejić. 2020-09-27. Two-root Riemannian Manifolds. https://arxiv.org/abs/2009.12834

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