Geodesic
Manifolds of almost nonnegative curvature
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 201-260

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The paper contains a systematic exposition of results due to the author and K. Fukaya on manifolds of almost nonnegative curvature. The final part contains several conjectures and modern problems. Bibl. 78 titles. 
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     author = {Takao Yamaguchi},
     title = {Manifolds of almost nonnegative curvature},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {201--260},
     publisher = {mathdoc},
     volume = {234},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a15/}
}
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Takao Yamaguchi. Manifolds of almost nonnegative curvature. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 201-260. http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a15/