The heat kernel and the spectrum of a class of nilmanifolds
The heat kernel and the spectrum of a class of nilmanifolds
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一类尼尔流形的热核和谱
DOI：
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发表时间：
1996
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影响因子：
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通讯作者：
Kenro Furutani
中科院分区：
文献类型：
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作者：
Kenro Furutani
Let L be a lattice in R{sup n}, then the Jacobi identity is written as (1.1) {summation}{sub {gamma}}{epsilon}{sub L} e{sup -4}{pi}{sup 2}{parallel}{sup 2}t = Vol(R{sup n}/L)/(4{pi}t){sup n/2} {summation}{sub {gamma}}{epsilon}{sub L} e{sup -{parallel}{sup 2}/4t}. As is well-known, the left side of (1.1) is the trace of the heat kernel on the flat torus R{sup n}/L and the right side reveals the lengths of closed geodesics on it corresponding to each element in L.
Let L be a lattice in R{sup n}, then the Jacobi identity is written as (1.1) {summation}{sub {gamma}}{epsilon}{sub L} e{sup -4}{pi}{sup 2}{parallel}{sup 2}t = Vol(R{sup n}/L)/(4{pi}t){sup n/2} {summation}{sub {gamma}}{epsilon}{sub L} e{sup -{parallel}{sup 2}/4t}. As is well-known, the left side of (1.1) is the trace of the heat kernel on the flat torus R{sup n}/L and the right side reveals the lengths of closed geodesics on it corresponding to each element in L.