The integral of the top dimensional term of the multiplicative sequence of Pontryagin forms associated to an even formal power series is calculated for special Riemannian metrics on the unit ball of a hermitean vector space. Using this result we calculate the generating function of the reduced Dirac and signature η–invariants for the family of Berger metrics on the odd dimensional spheres.

中文翻译：

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关于Berger球的η不变量

对于厄米向量空间上单位球上的特殊黎曼度量，计算出与偶数形式幂级数相关的庞特里亚金形式的乘法序列的顶级项的积分。利用这个结果，我们可以计算出奇数维球面上Berger度量族的简化Dirac和签名η-不变量的生成函数。