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scikit-learn's contrib package, imbalanced-learn, has a function, geometric_mean_score(), which has the following in its documentation:

The geometric mean (G-mean) is the root of the product of class-wise sensitivity. This measure tries to maximize the accuracy on each of the classes while keeping these accuracies balanced. For binary classification G-mean is the squared root of the product of the sensitivity and specificity. For multi-class problems it is a higher root of the product of sensitivity for each class.

Why is sensitivity and specificity used for binary classification? In the sources below, geometric mean is defined as the geo mean of precision and recall.

Cross Validated answer

g-mean is defined as $g = \sqrt{\ Precision * Recall\ }$

Towards DS: Beyond Accuracy

There are other metrics for combining precision and recall, such as the Geometric Mean of precision and recall, but the F1 score is the most commonly used.

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