AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (247 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Some rigidity theorems for totally real submanifolds in complex space forms

Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabi; fmalghamdi@uj.edu.sa
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia; fyalmofarrah@pnu.edu.sa
Department of Mathematics, King Khalid University, 900 Abha, Saudi Arabia; akali@kku.edu.sa, mbouleryah@kku.edu.sa
Show Author Information

Abstract

A study of the relationship between pseudo-umbilical totally real submanifolds and minimal totally real submanifolds in complex space forms is presented in this paper. The paper studies totally real submanifolds in complex space forms. The moving-frame method and the DDVV inequality (a conjecture for the Wintgen inequality on Riemannian submanifolds in real space forms proven by P.J. De Smet, F. Dillen, L. Verstraelen, and L. Vrancken) are used to obtain some rigidity theorems and an integral inequality, improving the associated results.

Keywords

complex space form, totally real submanifoldssecond fundamental formpinching theorems
CLC number: 53C21, 53C50, 53C25

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 8191-8202
DOI: 10.3934/math.2025376

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Alghamdi F, Mofarreh F, Ali A, et al. Some rigidity theorems for totally real submanifolds in complex space forms. AIMS Mathematics, 2025, 10(4): 8191-8202. https://doi.org/10.3934/math.2025376

5

Views

0

Downloads

0

Crossref

0

Web of Science

1

Scopus
Received: 01 January 2025
Revised: 23 February 2025
Accepted: 03 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)