Is there a way to scroll the page vertically or horizontally just on cursor movement?
I don't understand the question. Do you have an example site you can show us?
Most sites can be scrolled by either of 2 ways:
1) The default browser scrollbars.
2) Keyboard arrows / PageUp or PageDown keys.
Also many users are on mobile devices which have no mouse / cursor.
no there is not because the browser is not (always) allowed to track cursers
you can have elements on your site react to scroll i.e, as the page scrolls down an animation plays or a image becomes visable
That's extactly what I'm looking for!