Artículos de revistas
(1, 2)-symplectic Metrics, Flag Manifolds And Tournaments
Registro en:
Bulletin Of The London Mathematical Society. , v. 34, n. 6, p. 641 - 649, 2002.
246093
10.1112/S002460930200142X
2-s2.0-0036851549
Autor
Cohen N.
Negreiros C.J.C.
San Martin L.A.B.
Institución
Resumen
It has recently been shown by Mo and Negreiros that a necessary condition for an invariant almost complex structure on the complex full flag manifold double-struck F(n) to admit a (1, 2)-symplectic invariant metric is that its associated tournament be cone-free. In this paper, a canonical stair-shaped form is given for such tournaments, and this is applied to show that the condition is also sufficient; in the process, all the associated (1, 2)-symplectic metrics are described. 34 6 641 649 Black, M., Harmonic maps into homogeneous spaces (1991) Pitman Res. Notes Math. Ser., 255. , Longman, Harlow Borel, A., Kählerian coset spaces of semi-simple Lie groups (1954) Proc. Nat. Acad. Sci., 40, pp. 1147-1151 Borel, A., Hirzebruch, F., Characteristic classes and homogeneous spaces I (1958) Amer. J. Math., 80, pp. 458-538 Burstall, F.E., Salamon, S., Tournaments, flags and harmonic maps (1987) Math. Ann., 277, pp. 249-265 Cohen, N., Negreiros, C.J.C., San Martin, L.A.B., A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds Bol. Soc. Brasil. Mat. (N.S.), , to appear Eells, J., Salamon, S., Twistorial constructions of harmonic maps of surfaces into four manifolds (1985) Ann. Scuola Norm. Sup. Pisa (4), 12, pp. 589-640 Gray, A., Minimal varieties and almost Hermitian submanifolds (1965) Michigan Math. J., 2, pp. 273-287 Gray, A., Hervella, L.M., The sixteen classes of almost hermitian manifolds and their linear invariants (1980) Ann. Mat. Pura Appl., 123, pp. 35-58 Kobayashi, S., Nomizu, K., (1969) Foundations of differential geometry, 2. , Interscience Publishers Lichnerowicz, A., Applications harmoniques et variétés Kähleriennes (1970) Sympos. Math., 3, pp. 341-402. , Bologna Mo, X., Negreiros, C.J.C., Tournaments and geometry of full flag manifolds (2000) Proc. XI Brazilian Topology Meeting, , World Scientific Mo, X., Negreiros, C.J.C., (1, 2)-symplectic structures on flag manifolds (2000) Tôhoku Math. J., 52, pp. 271-282 Moon, J.W., (1968) Topics on tournaments, , Holt, Reinhart and Winston Negreiros, C.J.C., Some remarks about harmonic maps into flag manifolds (1988) Indiana Univ. Math. J., 37, pp. 617-636 Paredes, M., (2000) Aspectos da geometria complexa das variedades bandeira, , Ph.D. thesis, State University of Campinas Paredes, M., Families of (1, 2)-symplectic metrics on flag manifolds (2002) Int. J. Math. Math. Sci., 29, pp. 651-664 Salamon, S., Harmonic and holomorphic maps (1986) Lecture Notes in Math., 1164. , Springer San Martin, L.A.B., Negreiros, C.J.C., Invariant almost Hermitian structures on flag manifolds Adv. Math., , to appear Wolf, J.A., Gray, A., Homogeneous spaces defined by Lie group automorphisms II (1968) J. Diff. Geom., 2, pp. 115-159