Rigidity and vanishing results on totally real submanifolds under $L^p$-integrable conditions

TL;DR

This paper revises and extends previous results on rigidity and vanishing properties of totally real minimal submanifolds in complex space forms, focusing on $L^p$-integrable conditions and broadening the applicable range of $p$.

Contribution

It generalizes earlier results by Cuong et al. on rigidity and vanishing properties, extending the range of $p$ for $L^p$-integrable conditions on such submanifolds.

Findings

Extended the range of $p$ for $L^p$-integrability conditions.

Revised rigidity and vanishing results for totally real minimal submanifolds.

Improved understanding of geometric properties under integrability assumptions.

Abstract

In this paper, we revise some results on rigidity and vanishing properties obtained by \textit{Cuong et.al} in \cite{CDS24} on $n$-dimensional totally real minimal submanifolds $M$ immersed in complex space forms $\widetilde{M}^n(c)$, for $c\leq0$. We extend the range of $p$ in their paper.