Duke Mathematical Journal

The stable $4$-dimensional geometry of the real Grassmann manifolds

Weiqing Gu
Source: Duke Math. J. Volume 93, Number 1 (1998), 155-178.
First Page: Show Hide
Primary Subjects: 53C42
Secondary Subjects: 53C40
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077230640
Mathematical Reviews number (MathSciNet): MR1620092
Zentralblatt MATH identifier: 0943.53036
Digital Object Identifier: doi:10.1215/S0012-7094-98-09306-1

References

[B] Marcel Berger, Du côté de chez Pu, Ann. Sci. École Norm. Sup. (4) 5 (1972), 1–44.
Mathematical Reviews (MathSciNet): MR46:8119
Zentralblatt MATH: 0227.52005
[Bo] Armand Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math. (2) 57 (1953), 115–207.
Mathematical Reviews (MathSciNet): MR14,490e
Zentralblatt MATH: 0052.40001
Digital Object Identifier: doi:10.2307/1969728
[dR] Georges de Rham, On the area of complex manifolds, Global Analysis: Papers in Honor of K. Kodaira, Univ. Tokyo Press, Tokyo, 1969, pp. 141–148.
Mathematical Reviews (MathSciNet): MR40:6599
Zentralblatt MATH: 0192.44102
[D1] Dennis De Turck, et al., You cannot hear the mass of a homology class, Comment. Math. Helv. 64 (1989), no. 4, 589–617.
Mathematical Reviews (MathSciNet): MR90k:58233
Zentralblatt MATH: 0694.53037
Digital Object Identifier: doi:10.1007/BF02564696
[D2] Dennis DeTurck, et al., Conformal isospectral deformations, Indiana Univ. Math. J. 41 (1992), no. 1, 99–107.
Mathematical Reviews (MathSciNet): MR93c:58218
Zentralblatt MATH: 0742.58055
Digital Object Identifier: doi:10.1512/iumj.1992.41.41006
[D3] Dennis DeTurck, et al., The geometry of isospectral deformations, Differential Geometry: Riemannian Geometry (Los Angeles, Calif., 1990), Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, 1993, pp. 135–154.
Mathematical Reviews (MathSciNet): MR94b:58096
Zentralblatt MATH: 0811.53035
[D4] Dennis DeTurck, et al., The inaudible geometry of nilmanifolds, Invent. Math. 111 (1993), no. 2, 271–284.
Mathematical Reviews (MathSciNet): MR93k:58222
Zentralblatt MATH: 0779.53026
Digital Object Identifier: doi:10.1007/BF01231288
[F] Herbert Federer, Geometric Measure Theory, Grundlehren Math. Wiss., vol. 153, Springer-Verlag, New York, 1969.
Mathematical Reviews (MathSciNet): MR41:1976
Zentralblatt MATH: 0176.00801
[GMM] Herman Gluck, Dana Mackenzie, and Frank Morgan, Volume-minimizing cycles in Grassmann manifolds, Duke Math. J. 79 (1995), no. 2, 335–404.
Mathematical Reviews (MathSciNet): MR96d:53061
Zentralblatt MATH: 0837.53035
Digital Object Identifier: doi:10.1215/S0012-7094-95-07909-5
Project Euclid: euclid.dmj/1077285156
[GMZ] Herman Gluck, Frank Morgan, and Wolfgang Ziller, Calibrated geometries in Grassmann manifolds, Comment. Math. Helv. 64 (1989), no. 2, 256–268.
Mathematical Reviews (MathSciNet): MR90h:53077
Zentralblatt MATH: 0681.53039
Digital Object Identifier: doi:10.1007/BF02564674
[GZ] Herman Gluck and Wolfgang Ziller, On the volume of a unit vector field on the three-sphere, Comment. Math. Helv. 61 (1986), no. 2, 177–192.
Mathematical Reviews (MathSciNet): MR87j:53063
Zentralblatt MATH: 0605.53022
Digital Object Identifier: doi:10.1007/BF02621910
[HL] Reese Harvey and H. Blaine Lawson, Jr., Calibrated geometries, Acta Math. 148 (1982), 47–157.
Mathematical Reviews (MathSciNet): MR85i:53058
Zentralblatt MATH: 0584.53021
Digital Object Identifier: doi:10.1007/BF02392726
[M] Frank Morgan, Geometric Measure Theory: A Beginner's Guide, Academic Press, Boston, 1988.
Mathematical Reviews (MathSciNet): MR89f:49036
Zentralblatt MATH: 0671.49043
[P] Lui-Hua Pan, Existence and uniqueness of volume-minimizing cycles in Grassmann manifolds, Ph.D. thesis, University of Pennsylvania, 1992.
[Wi] W. Wirtinger, Eine Determinantenidentitat und ihre Anwendung auf analytische Gebilde und Hermitesche Massbestimmung, Monatsh. Math. Phys. 44 (1936), 343–365.
Zentralblatt MATH: 0015.07602
[Wo] Joseph A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967.
Mathematical Reviews (MathSciNet): MR36:829
Zentralblatt MATH: 0162.53304

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?