Geodesic
Stationarity of curvature of two-dimensional totally geodesic submanifolds in the Grassmannian of bevectors
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 175-185 Cet article a éte moissonné depuis la source Math-Net.Ru

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An infinitesimal criterion indicating when a two-dimensional submanifold of a Riemannian symmetric space is totally geodesic is given. As an application, the classification of two-dimensional totally geodesic submanifolds of the Grassmannian of bevectors is given in a new way, and it is proved that the section al curvature takes stationary values on tangent spaces of such submanifolds. 
@article{ZNSL_2001_280_a11,
     author = {S. E. Kozlov},
     title = {Stationarity of curvature of two-dimensional totally geodesic submanifolds in the {Grassmannian} of bevectors},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {175--185},
     year = {2001},
     volume = {280},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a11/}
}
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S. E. Kozlov. Stationarity of curvature of two-dimensional totally geodesic submanifolds in the Grassmannian of bevectors. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 175-185. http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a11/