Geodesic
Sectional curvatures and the separation set of the complex projective space in its Pl\"ucker model
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 186-193

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The Plücker embedding of the complex projective space $\mathbb CP^{k-1}$ in the Grassmannian $G^+_{2,2k}$ of bivectors is used for proving several theorems on the relationship between the complex structure of $\mathbb CP^{k-1}$ and its Riemannian geometry. It is shown that the separation set of $\mathbb CP^{k-1}$ in the Plücker model is a face of $G^+_{2,2k}$ for a certain calibration. 
@article{ZNSL_2001_280_a12,
     author = {S. E. Kozlov and M. Yu. Nikanorova},
     title = {Sectional curvatures and the separation set of the complex projective space in its {Pl\"ucker} model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {186--193},
     publisher = {mathdoc},
     volume = {280},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a12/}
}
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S. E. Kozlov; M. Yu. Nikanorova. Sectional curvatures and the separation set of the complex projective space in its Pl\"ucker model. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 186-193. http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a12/