Used in binary classification
G-mean = Sqrt of TPR*TNR
AUC is an error or performance metric very useful for replacing accuracy in binary classification with strong class imbalance. https://thedigitalskye.com/2021/04/19/6-useful-metrics-to-evaluate-binary-classification-models/
Geometric mean in general isn’t an error or performance metric, but is just an alternative to an arithmetic mean that’s robust to different normalization schemes.
Metrics in binary classification https://neptune.ai/blog/evaluation-metrics-binary-classification