Abstract
A canonical bijection between the set of extreme points of the comass-unit sphere \(S_{2,2k}^* \subset \Lambda^2 (\mathbb{R}^{2k})\) and the manifold of orthogonal complex structures in \(\mathbb{R}^{2k}\) is described, under which unitary bases correspond to decompositions of the forms realizing the conjugate norm of the mass. This correspondence is used for obtaining a classification of faces of the sphere \(S_{2,n}^*\) and the known classification of faces of the set polar to \(S_{2,n}^*\). Bibliography: 10 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
F. Morgan, “Area-minimizing surfaces, faces of grassmannians, and calibrations” Math. Month., 95, 813-822 (1988).
H. Whitney, Geometric Integration Theory, Princeton Univ. Press, Princeton, New Jersey (1957).
G. Federer and U. H. Fleming, “Normal and integer currents” Ann. Math., 72, 458-520 (1960).
S. E. Kozlov, “Geometry of real Grassmann manifolds. Part III” Zap. Nauchn. Semin. POMI, 246, 108-129 (1997).
F. Morgan, “On the singular structure of two-dimensional area minimizing surfaces in ℝn” Math. Ann., 261, 101-110 (1982).
J. Dadok, R. Harvey, and F. Morgan, “Calibrations on ℝ8” Trans. Math., 307, 1-40 (1988).
T. Bonnesen and W. Fenchel, Theorie der Konvexen Körper, Berlin, Springer (1934); New York (1948).
S. E. Kozlov, “Orthogonally congruent bivectors” Ukr. Geom. Sb., 27, 68-75 (1984).
G. Federer, Geometric Measure Theory, Springer, Berlin (1969).
S. E. Kozlov, “Geometry of real Grassmann manifolds. Part IV” Zap. Nauchn. Semin. POMI, 252, 78-103 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Glushakov, A.N., Kozlov, S.E. Geometry of the Sphere of Calibrations of Degree Two. Journal of Mathematical Sciences 110, 2776–2782 (2002). https://doi.org/10.1023/A:1015394010951
Issue Date:
DOI: https://doi.org/10.1023/A:1015394010951