On Differential Equations Characterizing Legendrian Submanifolds of Sasakian Space Forms

Rifaqat Ali, Fatemah Mofarreh, Nadia Alluhaibi, Akram Ali and Iqbal Ahmad
Additional contact information
Rifaqat Ali: Department of Mathematics, College of Sciences and Arts, Muhayil, King Khalid University, Abha 9004, Saudi Arabia
Fatemah Mofarreh: Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia
Nadia Alluhaibi: Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah 21911, Saudi Arabia
Akram Ali: Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia
Iqbal Ahmad: College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia

Mathematics, 2020, vol. 8, issue 2, 1-10

Abstract: In this paper, we give an estimate of the first eigenvalue of the Laplace operator on minimally immersed Legendrian submanifold N n in Sasakian space forms N ˜ 2 n + 1 ( ? ) . We prove that a minimal Legendrian submanifolds in a Sasakian space form is isometric to a standard sphere S n if the Ricci curvature satisfies an extrinsic condition which includes a gradient of a function, the constant holomorphic sectional curvature of the ambient space and a dimension of N n . We also obtain a Simons-type inequality for the same ambient space forms N ˜ 2 n + 1 ( ? ) .

Keywords: legendrian submanifolds; sasakian space forms; obata differential equation; isometric immersion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/150/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/150/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:150-:d:311411

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().