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International Journal of Mathematics and Mathematical Sciences - Volume 24 2000, Issue 1, Pages 43-48

Department of Mathematics, Hangzhou Teachers' College, 96 Wen Yi Road, Hangzhou 310012, China

Received 23 April 1999

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give some estimates of the first eigenvalue of the Laplacianfor compact and non-compact submanifold immersed in the Euclidean space byusing the square length of the second fundamental form of the submanifoldmerely. Then some spherical theorems and a nonimmersibility theorem of Chernand Kuiper type can be obtained.

Author: Kairen Cai



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