Is there by any chance a web based app for viewing parametric curves and surfaces that arise in differential geometry to help visualization? Thanks.
I assume you are talking about curves/surfaces that are immersed in $\mathbb R^2$ or $\mathbb R^3$. More abstract or higher dimensional curves/surfaces would be a bit harder to work with.
As HallaSurvivor mentioned in a comment, Wolfram|Alpha's plotting and graphics capabilities include static plots of parametric surfaces and curves in 3d, or curves in 2d.
If you want something more interactive, Desmos's graphing calculator works well for 2D. The Desmos learn page on "parametric equations" links to an example page including a family of parametric curves with an extra parameter $a$ that can be modified with a slider to display different curves. And the Desmos learn page on "points" links to an example page including a parametric curve shown one point at a time where the parameter can be controlled with a slider. Pressing the play button ▶ will have the parameter increase at a fixed speed so the nature of the parametrization can be understood in motion.
Finally, the Math3D app has many features similar to Desmos, plus some additional features built in (e.g. vectors), and can handle interactive/animated parametrized curves and surfaces in 3D, as shown in the Math3D example for a ruled hyperboloid (of one sheet).
Edit: Thanks to Semiclassical's comment for reminding me about the GeoGebra 3d calculator which has similar functionality (and can do a lot more with some complicated inputs). Geogebra has curve and surface commands for parametric constructions. You can see both with some sliders in a demonstration by matheagle. You can even code a 2d slider to control a pair of parameters for a surface, as exemplified in Lenore Horner's demonstration.
I didn't mention this originally because there is a much steeper barrier to entry, but CoCalc has a free plan and could be used for graphing on the web if you're already comfortable with a relevant programming language. See one collection of examples (including a graph of a parametrized surface) using SageMath and one collection (including a parametrized triangulated Möbius strip) using matplotlib in Python.