Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 7, Tome 280 (2001), pp. 175-185
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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/
@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/}
}
TY - JOUR
AU - S. E. Kozlov
TI - Stationarity of curvature of two-dimensional totally geodesic submanifolds in the Grassmannian of bevectors
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2001
SP - 175
EP - 185
VL - 280
UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a11/
LA - ru
ID - ZNSL_2001_280_a11
ER -
%0 Journal Article
%A S. E. Kozlov
%T Stationarity of curvature of two-dimensional totally geodesic submanifolds in the Grassmannian of bevectors
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 175-185
%V 280
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_280_a11/
%G ru
%F ZNSL_2001_280_a11
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.
