A special case of the NON-inverting amplifier has Rf = 0.0 ohms. That is, the op amp output is connected directly ("short circuit") to the inverting input and Ri is removed entirely (i.e., Ri = infinite ohms; "open circuit").
This configuration is called a "unity gain buffer", or a "voltage follower".
What is the voltage gain of this configuration? What is its input impedance?