Abstract
It is shown that if ann-dimensional (n≧3) Riemannian manifold admitsr≧2 locally symmetric vector fields (LSVF's), then it is aV(k)-space. In particular, ifr=n−1 then the manifold is a space of constant curvature. In the case of a 3-dimensional Riemannian manifold a close connection between LSVF's and eigenvectors of the Ricci tensor is found.
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Gauchman, H. On locally symmetric vector fields on Riemannian manifolds. Israel J. Math. 33, 37–51 (1979). https://doi.org/10.1007/BF02760531
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DOI: https://doi.org/10.1007/BF02760531