Marlio PAREDES, PINZQN Sofia

On the codifferential of the Kähler form and cosymplectic metrics on maximal flag manifolds

Using moving frames we obtain a formula to calculate the codifferential of the Kähler form on a maximal flag manifold. We use this formula to obtain some differential type conditions so that a metric on the classical maximal flag manifold be cosymplectic.

Anahtar Kelimeler:

Codifferential, Kähler form, flag manifolds, differential forms.

On the codifferential of the Kähler form and cosymplectic metrics on maximal flag manifolds

Keywords:

Codifferential, Kähler form, flag manifolds, differential forms.,

PDF

___

i
Burstall, F. E., Salamon, S.: Tournaments, ﬂags and harmonic maps. Math. Ann. 277, 249–265 (1987).
Chern, S. S., Wolfson, J. G.: Harmonic maps of the two–sphere into a complex Grassmann manifold II. Ann. of Math. 125, 301–335 (1987).
Cohen, N., Negreiros, C. J. C., Paredes, M., Pinz´on, S., San Martin L. A. B.: f –Structures on the classical ﬂag manifold which admit (1, 2) –symplectic metrics. Tohoku Math. J. (2) 57, 261–271 (2005)
Cohen, N., Negreiros, C. J. C., San Martin, L. A. B.: (1, 2) –symplectic metrics, ﬂag manifolds and tournaments. Bull. London Math. Soc. 34, 641–649 (2002).
Cohen, N., Paredes, M., Pinz´on, S.: Locally transitive tournaments and the classiŞcation of (1, 2) –symplectic metrics on maximal ﬂag manifolds. Illinois J. Math. 48, 1405–1415 (2004).
Gray, A., Hervella, L. M.: The sixteen classes of almost Hermitian manifolds and their linear invariants. Ann. Mat. Pura Appl. (4) 123, 35–58 (1980).
Griﬃths, P., Harris, J.: Principles of algebraic geometry. New York. John Wiley & Sons 1978.
Mo, X., Negreiros, C. J. C.: (1, 2) -Symplectic structures on ﬂag manifolds. Tohoku Math. J. (2) 52, 271–282 (2000).
Moon, J. W.: Topics on tournaments. New York. Holt, Rinehart and Winston 1968.
Paredes, M.: Aspectos da geometria complexa das variedades bandeira. Ph.D. Thesis, State University of Campinas, Brazil, 2000.
Paredes, M.: Some results on the geometry of full ﬂag manifolds and harmonic maps. Rev. Col. Mat. 34, 57–89 (2000).
Paredes, M.: Families of (1, 2) –symplectic metrics on full ﬂag manifolds. Internat. J. Math. Math. Sci. 29, 651–664 (2002).
San Martin, L. A. B., Negreiros, C. J. C.: Invariant almost Hermitian structures on ﬂag manifolds. Adv. Math. , 277–310 (2003). Marlio PAREDES
School of Science and Technology University of Turabo Gurabo, PR 00778-3030, USA e-mail: maparedes@suagm.edu Sof´ıa PINZ ´ON
Escuela de Matem´aticas Universidad Industrial de Santander Bucaramanga, Carrera 27 - Calle 9, Colombia e-mail: spinzon@uis.edu.co