For a manifold with a metric (M,g), for f: M - M demand f is a diffeomorphism that preserves the metric.

This is an isometry.

Metric is flat iff .

source psfile jl@crush.caltech.edu index metric_compatible_connection string_world-sheet_action duality_transformation Fucci-Hansen_metric hermitian_metric Euclidean_space complex_metric Weyl_rescaling inner_product weyl_tensor vielbeinsl isometry spinor