Eigenvalues of the Laplacian of Warped Product
Eigenvalues of the Laplacian of Warped Product
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翘曲产品拉普拉斯算子的特征值
DOI：
10.3836/tjm/1270216086
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发表时间：
1980
影响因子：
0.6
通讯作者：
K. Tsukada
中科院分区：
文献类型：
--
作者：
K. Tsukada
设Spec $（M，g）=\{0=\lambda_{0}<\lambda_{1}\leqq x_{2}\leqq\cdots\}$是$\triangle$的特征值集合，其中每个特征值重复的次数与其重数相同。设$（B，g）$和$（F，h）$是黎曼流形，$f>0$是B$上的可微函数.考虑乘积流形$B\times F$及其投影$\pi：B\times F\rightarrow B$和$\eta：B\times F\rightarrow F$。翘曲积$M=BX_{f}F$是流形$B\times F$，其具有黎曼结构$\overline{g}$，使得
Let Spec $(M, g)=\{0=\lambda_{0}<\lambda_{1}\leqq x_{2}\leqq\cdots\}$ be the set of eigenvalues of $\triangle$ , where each eigenvalue is repeated as many times as its multiplicity. Let $(B, g)$ and $(F, h)$ be Riemannian manifolds and $f>0$ a differentiable function on $B$. Consider the product manifold $B\times F$ with its projections $\pi:B\times F\rightarrow B$ and $\eta:B\times F\rightarrow F$. The warped product $M=BX_{f}F$ is the manifold $B\times F$ furnished with the Riemannian structure $\overline{g}$ such that