Pseudo-parallel Lagrangian submanifolds are semi-parallel

TL;DR

This paper proves that all Lagrangian pseudo-parallel submanifolds in complex space forms of dimension at least 3 are necessarily semi-parallel, confirming a conjecture in differential geometry.

Contribution

It establishes a significant geometric property linking pseudo-parallelism and semi-parallelism for Lagrangian submanifolds in complex space forms.

Findings

All Lagrangian pseudo-parallel submanifolds are semi-parallel in complex space forms of dimension ≥ 3.

Confirms a conjecture by Chacon and Lobos.

Advances understanding of submanifold geometry in complex space forms.

Abstract

We prove a conjecture formulated by Pablo M. Chacon and Guillermo A. Lobos in [Pseudo-parallel Lagrangian submanifolds in complex space forms, Differential Geom. Appl.] stating that every Lagrangian pseudo-parallel submanifold of a complex space form of dimension at least 3 is semi-parallel.