Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

Xing, Cheng; Yin, Jiabin

doi:10.1007/s12220-023-01481-w

J Geom Anal

2023

DOI: 10.1007/s12220-023-01481-w

|View full text |Cite

Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

Cheng Xing,

Jiabin Yin

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On conformally flat minimal Legendrian submanifolds in the unit sphere

Li,

Xing,

Yin

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

This paper is concerned with the study on an open problem of classifying conformally flat minimal Legendrian submanifolds in the $(2n+1)$ -dimensional unit sphere $\mathbb {S}^{2n+1}$ admitting a Sasakian structure $(\varphi,\,\xi,\,\eta,\,g)$ for $n\ge 3$ , motivated by the classification of minimal Legendrian submanifolds with constant sectional curvature. First of all, we completely classify such Legendrian submanifolds by assuming that the tensor $K:=-\varphi h$ is semi-parallel, which is introduced as a natural extension of $C$ -parallel second fundamental form $h$ . Secondly, such submanifolds have also been determined under the condition that the Ricci tensor is semi-parallel, generalizing the Einstein condition. Finally, as direct consequences, new characterizations of the Calabi torus are presented.

show abstract

On conformally flat minimal Legendrian submanifolds in the unit sphere

Li,

Xing,

Yin

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Some Optimal Inequalities for Anti-invariant Submanifolds of the Unit Sphere

Cited by 1 publication

References 30 publications

On conformally flat minimal Legendrian submanifolds in the unit sphere

On conformally flat minimal Legendrian submanifolds in the unit sphere

Contact Info

Product

Resources

About