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Thanks for reporting this bug! It is now tracked at https://trac.sagemath.org/ticket/31904 .

An immediate fix is to force the evaluation of the map Cyl2tocylindrical in the chart cartesian by a call to display() just before the computation of the induced metric:

Cyl2tocylindrical.display()

Then

C2g = C2.induced_metric()
C2g.display()

displays the expected result.

Thanks for reporting this bug! It is now tracked at https://trac.sagemath.org/ticket/31904 .

An immediate fix is to force the evaluation of the map Cyl2tocylindrical in the chart cartesian by a call to display() just before the computation of the induced metric:

Cyl2tocylindrical.display()

Then

C2g = C2.induced_metric()
C2g.display()

displays the expected result.