International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 1, Pages 43-48
doi:10.1155/S0161171200003306
First eigenvalue of submanifolds in Euclidean space
Kairen Cai
Department of Mathematics, Hangzhou Teachers' College, 96 Wen Yi Road, Hangzhou 310012, China
Abstract
We give some estimates of the first eigenvalue of the Laplacian for compact and non-compact submanifold immersed in the Euclidean space by using the square length of the second fundamental form of the submanifold merely. Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.