THE FIRST EIGENVALUE OF AN IRREDUCIBLE HOMOGENEOUS MANIFOLD
Citation：
Shen Zhongmin.THE FIRST EIGENVALUE OF AN IRREDUCIBLE HOMOGENEOUS MANIFOLD[J].Chinese Annals of Mathematics B,1988,9(3):270~273
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Authors：
Shen Zhongmin;
Abstract：
Let $M$ be an n-dimensional compact minimal submanifold in the unit sphere. It is shown that the dismeter and volnme of $M$ satisfy
$$\[d \ge \frac{\pi }{2} + C(n)\frac{{{d^n}}}{{{d^n} + V}}\]$$
An application is that if $M$ is an n-dimensional compact irreducible homogeneous manifold, the first eigenvalue $\[{\lambda _1}\]$ of $M$ satisfies
In the above two eases, $\[C{(n)^'}\]$ are the same constants depending only on n.
