Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T05:33:05.788Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonexistence of stable currents in submanifolds of a product of two spheres

Published online by Cambridge University Press:  17 April 2009

Xue-shan Zhang
Xue-shan Zhang
Affiliation:
Department of Mathematics, Xian Institute of Metallurgy and Construction Engineering, Xian 710055, Peoples Republic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By using techniques of the calculus of variations in geometric measure theory, we investigate the nonexistence of stable integral currents in Sn1 × Sn2 and its immersed submanifolds. Several vanishing theorems concerning the homology group of these manifolds are established.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 325 - 336
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Chen, B.-Y., Geometry of submanifolds (Dekker, New York, 1973).Google Scholar
[2]Federer, H. and Fleming, W., ‘Normal and integral currents’, Ann. of Math. 72 (1960), 458–520.CrossRefGoogle Scholar
[3]Lawson, H.B. and Simons, J., ‘On stable currents and their application to global problems in real and complex geometry’, Ann. of Math. 98 (1973), 427–450.CrossRefGoogle Scholar
[4]Xin, Y.-L., ‘An application of integral currents to the vanishing theorems’, Sci. Sinica Ser. A 27 (1984), 233–241.Google Scholar