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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
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Abstract

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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