Minimality of a Kind of Pseudo-Umbilical Totally Real Submanifolds in Non-Flat Complex Space Forms

TL;DR

This paper proves that pseudo-umbilical, totally real submanifolds with flat normal connection in non-flat complex space forms are necessarily minimal, advancing understanding of their geometric properties.

Contribution

It establishes a minimality result for a specific class of submanifolds in complex space forms, linking pseudo-umbilical condition and flat normal connection.

Findings

Pseudo-umbilical totally real submanifolds with flat normal connection are minimal in non-flat complex space forms.

The study clarifies the geometric structure of such submanifolds in complex space forms.

The result contributes to the classification of submanifolds with special curvature properties.

Abstract

In this paper, by studying the position of umbilical normal vectors in the normal bundle, we prove that pseudo-umbilical totally real submanifolds with flat normal connection in non-flat complex space forms must be minimal.