| Summary: | In this paper, we have parameterized a timelike (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k</mi><mi>e</mi></mrow></semantics></math></inline-formula>) circular surface (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">CI</mi><mspace width="4pt"></mspace><mi mathvariant="italic">surface</mi></mrow></semantics></math></inline-formula>) and have obtained its geometric properties, including striction curves, singularities, Gaussian and mean curvatures. Afterward, the situation for a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">T</mi><mi>l</mi><mi>i</mi><mi>k</mi><mi>e</mi></mrow></semantics></math></inline-formula> roller coaster surface (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">RCO</mi><mspace width="4pt"></mspace><mi mathvariant="italic">surface</mi></mrow></semantics></math></inline-formula>) to be a flat or minimal surface is examined in detail. Further, we illustrate the approach’s outcomes with a number of pertinent examples.
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