Minimal Surfaces With Special Forms In Sol₃

In this paper, we use the method of analysis and ordinary differential equation to study minimal surfaces with the form: (1) z= f(x)+g(y), (2) y =f(x)+g(z),(3) x = f(y) + g(z), (4) z = f(x)g(y), (5) y , f(x)g(z) and (6) x = f(y)g(z)in Sol3 space, where f and g are smooth functions on some interval of R. We study each of these six kind of minimal surface geometry, and give the complete classification theorem, a total of 28 kinds of situations.