Some rigidity theorems for totally real submanifolds in complex space forms

Fatimah Alghamdi; Fatemah Mofarreh; Akram Ali; Mohamed Lemine Bouleryah; Fatimah Alghamdi; Fatemah Mofarreh; Akram Ali; Mohamed Lemine Bouleryah

doi:10.3934/math.2025376

AIMS Mathematics

2025, Volume 10, Issue 4: 8191-8202. doi: 10.3934/math.2025376

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Research article

Some rigidity theorems for totally real submanifolds in complex space forms

1.
Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabi; fmalghamdi@uj.edu.sa
2.
Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia; fyalmofarrah@pnu.edu.sa
3.
Department of Mathematics, King Khalid University, 900 Abha, Saudi Arabia; akali@kku.edu.sa, mbouleryah@kku.edu.sa

Received: 01 January 2025 Revised: 23 February 2025 Accepted: 03 March 2025 Published: 09 April 2025
MSC : 53C21, 53C50, 53C25

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.
- complex space form, totally real submanifolds,
- second fundamental form,
- pinching theorems
Citation: Fatimah Alghamdi, Fatemah Mofarreh, Akram Ali, Mohamed Lemine Bouleryah. Some rigidity theorems for totally real submanifolds in complex space forms[J]. AIMS Mathematics, 2025, 10(4): 8191-8202. doi: 10.3934/math.2025376

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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.

References

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