Special slant surfaces with non-constant mean curvature in 2-dimensional complex space forms

TL;DR

This paper classifies proper special slant surfaces with non-constant mean curvature in 2-dimensional complex space forms, extending previous classifications of constant mean curvature cases.

Contribution

It provides a complete classification of proper special slant surfaces with non-constant mean curvature in 2D complex space forms, filling a gap in geometric surface theory.

Findings

Complete classification of non-constant mean curvature cases

Extension of Chen's earlier work on constant mean curvature surfaces

New insights into the geometry of special slant surfaces

Abstract

In the late 1990s, B. Y. Chen introduced the notion of special slant surfaces in K\"{a}hler surfaces and classified non-minimal proper special slant surfaces with constant mean curvature in $2$-dimensional complex space forms. In this paper, we completely classify proper special slant surfaces with non-constant mean curvature in $2$-dimensional complex space forms.