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Geometry of real Grassmannian manifolds. III. (English. Russian original) Zbl 0918.53009
J. Math. Sci., New York 100, No. 3, 2254-2268 (2000); translation from Zalgaller, V. A. (ed.) et al., Geometry and topology. 2. Work collection. Sankt-Peterburg: Matematicheskij Institut Im. V. A. Steklova, Sankt-Peterburgskoe Otdelenie, RAN, Zap. Nauchn. Semin. POMI. 246, 108-129 (1997).
In a previous paper [S. E. Kozlov, ibid., 84-107 (1997; Zbl 0918.53008), see the preceding review], the author established a Plücker model for the Grassmannian manifolds \(G^+_{p,n}\). In the paper under review, stationary angles between (oriented or non-oriented) planes are introduced. The diameter and the injectivity radius of \(G^+_{p,n}\) are calculated. Finally, the closure of geodesics in \(G^+_{p,n}\) is determined.

MSC:
53B25 Local submanifolds
15A75 Exterior algebra, Grassmann algebras
53A20 Projective differential geometry
53C20 Global Riemannian geometry, including pinching
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