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The Pontryagin $4$-form


Authors: Jiri Dadok and Reese Harvey
Journal: Proc. Amer. Math. Soc. 127 (1999), 3175-3180
MSC (1991): Primary 49Q05, 53C35, 15A42
DOI: https://doi.org/10.1090/S0002-9939-99-05443-X
Published electronically: July 12, 1999
MathSciNet review: 1690980
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Abstract | References | Similar Articles | Additional Information

Abstract: The unit $4$-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 [Enhancements On Off] (What's this?)

  • [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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Additional Information

Jiri Dadok
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: dadok@hamlet.usc.indiana.edu

Reese Harvey
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77251
Email: harvey@math.rice.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05443-X
Received by editor(s): November 24, 1997
Published electronically: July 12, 1999
Communicated by: Christopher Croke
Article copyright: © Copyright 1999 American Mathematical Society

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