Sphere theorems for Lagrangian and Legendrian submanifolds
Jun Sun, Linlin Sun
TL;DR
This paper establishes new differentiable and topological sphere theorems for Lagrangian submanifolds in Kähler manifolds and Legendrian submanifolds in Sasaki space forms, advancing understanding of their geometric properties.
Contribution
It introduces novel sphere theorems specifically for Lagrangian and Legendrian submanifolds within their respective ambient spaces.
Findings
Proves differentiable sphere theorems for Lagrangian submanifolds
Establishes topological sphere theorems for Legendrian submanifolds
Provides conditions under which these submanifolds are topologically spheres
Abstract
In this paper, we prove some differentiable sphere theorems and topological sphere theorems for Lagrangian submanifolds in K\"ahler manifold and Legendrian submanifolds in Sasaki space form.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research