Artículos de revistas
Differential Geometry Of Grassmannians And The Plücker Map
Registro en:
Central European Journal Of Mathematics. , v. 10, n. 3, p. 873 - 884, 2012.
18951074
10.2478/s11533-012-0021-y
2-s2.0-84859162512
Autor
Anan'in S.
Grossi C.H.
Institución
Resumen
Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For 'hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the 'elliptic' case. © 2012 Versita Warsaw and Springer-Verlag Wien. 10 3 873 884 Anan'in, S., Gonçalves, E.C.B., Grossi, C.H., Grassmannians and conformal structure on absolutes, , http://arxiv.org/abs/0907.4469, Preprint available at Anan'in, S., Grossi, C., Coordinate-free classic geometries (2011) Mosc. Math. J., 11 (4), pp. 633-655 Borisenko, A.A., Nikolaevskii, Y.A., Grassmann manifolds and Grassmann image of submanifolds (1991) Russian Math. Surveys, 46 (2), pp. 45-94 do Carmo, M.P., Riemannian Geometry (1992) Math. Theory Appl., , Boston: Birkhäuser Gromov, M., Lawson Jr., H.B., Thurston, W., Hyperbolic 4-manifolds and conformally flat 3-manifolds (1988) Inst. Hautes Études Sci. Publ. Math., 68, pp. 27-45 Guilfoyle, B., Klingenberg, W., Proof of the Carathéodory conjecture by mean curvature flow in the space of oriented affine lines, , http://arxiv.org/abs/0808.0851, Preprint available at Kobayashi, S., Nomizu, K., (1969) Foundations of Differential Geometry. II, Interscience Tracts in Pure and Applied Mathematics, , New York-London-Sydney: John Wiley & Sons Kuiper, N.H., Hyperbolic 4-manifolds and tesselations (1988) Inst. Hautes Études Sci. Publ. Math., 68, pp. 47-76 Luo, F., Constructing conformally flat structures on some Seifert fibred 3-manifolds (1992) Math. Ann., 294 (3), pp. 449-458