The Pontryagin $4$-form
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- by Jiri Dadok and Reese Harvey PDF
- Proc. Amer. Math. Soc. 127 (1999), 3175-3180 Request permission
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
- Jiri Dadok and Reese Harvey, Calibrations associated with triality algebras (in preparation).
- Herman Gluck, Dana Mackenzie, and Frank Morgan, Volume-minimizing cycles in Grassmann manifolds, Duke Math. J. 79 (1995), no. 2, 335–404. MR 1344765, DOI 10.1215/S0012-7094-95-07909-5
- Herman Gluck, Frank Morgan, and Wolfgang Ziller, Calibrated geometries in Grassmann manifolds, Comment. Math. Helv. 64 (1989), no. 2, 256–268. MR 997365, DOI 10.1007/BF02564674
- Weiqing Gu, The stable 4-dimensional geometry of the real Grassmann manifolds, Duke Math. J. 93 (1998), no. 1, 155–178. MR 1620092, DOI 10.1215/S0012-7094-98-09306-1
- Reese Harvey and H. Blaine Lawson Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157. MR 666108, DOI 10.1007/BF02392726
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
- MR Author ID: 189057
- Email: harvey@math.rice.edu
- Received by editor(s): November 24, 1997
- Published electronically: July 12, 1999
- Communicated by: Christopher Croke
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1690980