Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

The Pontryagin -form

Author(s): Jiri Dadok; Reese Harvey
Journal: Proc. Amer. Math. Soc. 127 (1999), 3175-3180.
MSC (1991): Primary 49Q05, 53C35, 15A42
Posted: July 12, 1999
MathSciNet review: 1690980
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Abstract | References | Similar articles | Additional information

Abstract: The unit -planes on which the first Pontryagin form of the Grassmann manifolds achieves its maximum are determined. This is a shorter and unified proof of results first obtained in 1995 by H. Gluck et al. and in 1998 by W. Gu.

References:

[DH]: Jiri Dadok and Reese Harvey, Calibrations associated with triality algebras (in preparation).
[GMM]: Herman Gluck, Dana Mackenzie, and Frank Morgan, Volume-minimizing cycles in Grassmann manifolds, Duke Math. J. 79 (2) (1995), 335-404. MR 96d:53061
[GMZ]: Herman Gluck, Frank Morgan, and Wolfgang Ziller, Calibrated geometries in Grassmann manifolds, Comm. Math. Helv. 64 (1989), 256-268. MR 90h:53077
[G]: Weiqing Gu, The stable $4$ -dimensional geometry of the real Grassmann manifolds, Duke Math. J. 93 (1998), 155-178. MR 99e:53091
[HL]: Reese Harvey and H. Blaine Lawson, Jr., Calibrated geometries, Acta Math. 148 (1982), 47-157. MR 85i:53058

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