Geodesic
Knotted totally geodesic submanifolds in positively curved spheres
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 4, pp. 458-463
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A diffeomorphic to sphere three-manifold of positive sectional curvature with geodesics of given torus type is constructed. 
@article{JMAG_2000_7_4_a5,
     author = {Alexander Reznikov},
     title = {Knotted totally geodesic submanifolds in positively curved spheres},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {458--463},
     year = {2000},
     volume = {7},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2000_7_4_a5/}
}
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Alexander Reznikov. Knotted totally geodesic submanifolds in positively curved spheres. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 7 (2000) no. 4, pp. 458-463. http://geodesic.mathdoc.fr/item/JMAG_2000_7_4_a5/