Geodesic
Three-dimensional open Riemannian space of nonnegative curvature
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part II, Tome 66 (1976), pp. 103-113

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Let $V^3$ be a connected three-dimensional open complete Riemannian manifold with nonnegative sectional curvature. It is proved that if at some point all the sectional curvatures are positive, then $V^3$ is diffeomorphic to a Euclidean space $R^3$. 
@article{ZNSL_1976_66_a1,
     author = {Yu. D. Burago},
     title = {Three-dimensional open {Riemannian} space of nonnegative curvature},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {103--113},
     publisher = {mathdoc},
     volume = {66},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a1/}
}
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Yu. D. Burago. Three-dimensional open Riemannian space of nonnegative curvature. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part II, Tome 66 (1976), pp. 103-113. http://geodesic.mathdoc.fr/item/ZNSL_1976_66_a1/