caa a22 4500 463248341 CHVBK 20180405153332.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10455-006-9044-6 doi (NATIONALLICENCE)springer-10.1007/s10455-006-9044-6 On non-negatively curved metrics on open five-dimensional manifolds [Elektronische Daten] [Mikael Bengtsson, Valery Marenich] Let V n be an open manifold of non-negative sectional curvature with a soul Σ of co-dimension two. The universal cover $$\tilde N$$ of the unit normal bundle N of the soul in such a manifold is isometric to the direct product M n-2× R. In the study of the metric structure of V n an important role plays the vector field X which belongs to the projection of the vertical planes distribution of the Riemannian submersion $$\pi\!\!:V\to\Sigma$$ on the factor M in this metric splitting $$\tilde N = M\times R$$ . The case n=4 was considered in [Gromoll, D., Tapp, K.: Geom. Dedicata 99, 127-136 (2003)] where the authors prove that X is a Killing vector field while the manifold V 4 is isometric to the quotient of $$M^2\times (R^2,g_F)\times R$$ by the flow along the corresponding Killing field. Following an approach of [Gromoll, D., Tapp, K.: Geom. Dedicata 99, 127-136 (2003)] we consider the next case n=5 and obtain the same result under the assumption that the set of zeros of X is not empty. Under this assumption we prove that both M 3 and Σ3 admit an open-book decomposition with a bending which is a closed geodesic and pages which are totally geodesic two-spheres, the vector field X is Killing, while the whole manifold V 5 is isometric to the quotient of $$M^3\times (R^2,g_F)\times R$$ by the flow along corresponding Killing field. Springer Science + Business Media B.V., 2006 Open manifolds nationallicence Non-negative curvature nationallicence Bengtsson Mikael Högskolan I Kalmar, 391 82, Kalmar, Sweden aut Marenich Valery Högskolan I Kalmar, 391 82, Kalmar, Sweden aut Annals of Global Analysis and Geometry Kluwer Academic Publishers 31/2(2007-04-01), 213-221 0232-704X 31:2<213 2007 31 10455 https://doi.org/10.1007/s10455-006-9044-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10455-006-9044-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bengtsson Mikael Högskolan I Kalmar, 391 82, Kalmar, Sweden aut NATIONALLICENCE 700 1- Marenich Valery Högskolan I Kalmar, 391 82, Kalmar, Sweden aut NATIONALLICENCE 773 0- Annals of Global Analysis and Geometry Kluwer Academic Publishers 31/2(2007-04-01), 213-221 0232-704X 31:2<213 2007 31 10455 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer