A Wintgen type inequality for surfaces in 4D neutral pseudo-Riemannian space forms and its applications to minimal immersions

Abstract

Let $M$ be a space-like surface immersed in a 4-dimensional pseudo-Riemannian space form $R_2^4(c)$ with constant sectional curvature $c$ and index two. In the first part of this article, we prove that the Gauss curvature $K$, the normal curvature $K^D$, and mean curvature vector $H$ of $M$ satisfy the general inequality: $K+K^D\ge H,H+c$. In the second part, we investigate space-like minimal surfaces in $R_2^4(c)$ which satisfy the equality case of the inequality identically. Several classification results in this respect are then obtained.

arXiv comment13 pages

Cited by in corpus (1)

• On Wintgen ideal surfaces