A Geometry of real Grassmannian manifolds. Part~III
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 108-129
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A canonical decomposition for an element of the tangent fibration of Grassmannian manifold $G^+_{p,n}$ in its Plücker model is constructed. By means of the decomposition a concept of stationary angles between oriented planes is introduced and a connection with stationary angles in a nonoriented case is ascertained. A direct formula allowed to calculate the diameter and the radius of injectiveness of the manifold $G^+_{p,n}$ is given. A problem of the uniqueness of the above canonical decomposition has been reduced to a previously solved by the author similar problem of the decomposition of bivectors which realizes their mass. By virtue of a
developed technique a structure of the closure of an arbitrary geodesic in manifolds $G^+_{p,n}$ and $G_{p,n}$ was determined. The last result for manifolds $G_{p,n}$ was earlier announced by Wong without proof.
@article{ZNSL_1997_246_a5,
author = {S. E. Kozlov},
title = {A {Geometry} of real {Grassmannian} manifolds. {Part~III}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {108--129},
publisher = {mathdoc},
volume = {246},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a5/}
}
S. E. Kozlov. A Geometry of real Grassmannian manifolds. Part~III. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 108-129. http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a5/