Geodesic
On totally geodesic embeddings of 7-dimensional manifolds of positive sectional curvature
Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1853-1867

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Totally geodesic embeddings of an infinite series of 7-dimensional manifolds in 13-dimensional manifolds of positive sectional curvature are constructed in this paper. The topology of these embeddings is studied and the possibility of constructing new many-dimensional examples of manifolds of positive curvature is discussed. 
@article{SM_1996_187_12_a4,
     author = {I. A. Taimanov},
     title = {On totally geodesic embeddings of 7-dimensional manifolds of positive sectional curvature},
     journal = {Sbornik. Mathematics},
     pages = {1853--1867},
     publisher = {mathdoc},
     volume = {187},
     number = {12},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_12_a4/}
}
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I. A. Taimanov. On totally geodesic embeddings of 7-dimensional manifolds of positive sectional curvature. Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1853-1867. http://geodesic.mathdoc.fr/item/SM_1996_187_12_a4/