Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
873-884
Opis fizyczny
Daty
wydano
2012-06-01
online
2012-03-24
Twórcy
autor
- Universidade Estadual de Campinas, Ananin_Sasha@yahoo.com
autor
- Universidade de São Paulo, grossi@icmc.usp.br
Bibliografia
- [1] Anan’in S., Gonçalves E.C.B., Grossi C.H., Grassmannians and conformal structure on absolutes, preprint available at http://arxiv.org/abs/0907.4469
- [2] Anan’in S., Grossi C., Coordinate-free classic geometries, Mosc. Math. J., 2011, 11(4), 633–655
- [3] Borisenko A.A., Nikolaevskiı Yu.A., Grassmann manifolds and Grassmann image of submanifolds, Russian Math. Surveys, 1991, 46(2), 45–94 http://dx.doi.org/10.1070/RM1991v046n02ABEH002742
- [4] do Carmo M.P., Riemannian Geometry, Math. Theory Appl., Birkhäuser, Boston, 1992
- [5] Gromov M., Lawson H.B. Jr., Thurston W., Hyperbolic 4-manifolds and conformally flat 3-manifolds, Inst. Hautes Études Sci. Publ. Math., 1988, 68, 27–45 http://dx.doi.org/10.1007/BF02698540
- [6] Guilfoyle B., Klingenberg W., Proof of the Carathéodory conjecture by mean curvature flow in the space of oriented affine lines, preprint available at http://arxiv.org/abs/0808.0851
- [7] Kobayashi S., Nomizu K., Foundations of Differential Geometry. II, Interscience Tracts in Pure and Applied Mathematics, 15(2), John Wiley & Sons, New York-London-Sydney, 1969
- [8] Kuiper N.H., Hyperbolic 4-manifolds and tesselations, Inst. Hautes Études Sci. Publ. Math., 1988, 68, 47–76 http://dx.doi.org/10.1007/BF02698541
- [9] Luo F., Constructing conformally flat structures on some Seifert fibred 3-manifolds, Math. Ann., 1992, 294(3), 449–458 http://dx.doi.org/10.1007/BF01934334
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0021-y