We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.
@article{118493, author = {Kouei Sekigawa and Hiroshi Suga and Lieven Vanhecke}, title = {Four-dimensional curvature homogeneous spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {33}, year = {1992}, pages = {261-268}, zbl = {0763.53043}, mrnumber = {1189656}, language = {en}, url = {http://dml.mathdoc.fr/item/118493} }
Sekigawa, Kouei; Suga, Hiroshi; Vanhecke, Lieven. Four-dimensional curvature homogeneous spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 261-268. http://gdmltest.u-ga.fr/item/118493/
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