AI 中文总结
本文研究近接触伪度量流形的度量变分，推导了保持近接触伪度量结构的向量场条件，刻画了近伪余凯勒流形相关变分的性质并建立局部分解，还在统计结构下探讨该变分。
AI 中文摘要
对于近接触伪度量流形，我们以Meli-Ngakeu-Olea的思路研究度量的一种变分，该变分利用流形上的一个向量场定义，此过程会使度量的符号特征增加，正指标提升2。首先，我们推导该向量场需满足的条件，以保证所得流形仍为近接触伪度量流形；接着，研究近伪余凯勒流形的情况，特别地，我们获得了使基本形式保持闭的变分的几何刻画，并建立了其局部乘积分解；我们还在统计结构的框架下进一步研究该变分。
英文摘要
For an almost contact pseudo-metric manifold we study a variation of the metric in the spirit of Meli-Ngakeu-Olea. Such variation is defined using a vector field on the manifold and the procedure shifts the signature of the metric by increasing the positive index by two. First we derive conditions on the vector field for the obtained manifold to remain almost contact pseudo-metric. Then we study the cases of almost pseudo co-Kähler manifolds. In particular we obtain geometric characterizations of variations for which the fundamental form remains closed and establish a local decomposition into a product. We further investigate the variation in the setting of statistical structures.
