6
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

# Classification of $$\delta(2,n-2)$$-ideal Lagrangian submanifolds in $$n$$-dimensional complex space forms

Preprint

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### Abstract

It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold $$M$$ of a complex space form $$\tilde M^{n}(4c)$$ of constant holomorphic sectional curvature $$4c$$ satisfies the following optimal inequality: \begin{align*} \delta(2,n-2) \leq \frac{n^2(n-2)}{4(n-1)} H^2 + 2(n-2) c, \end{align*} where $$H^2$$ is the squared mean curvature and $$\delta(2,n-2)$$ is a $$\delta$$-invariant on $$M$$. In this paper we classify Lagrangian submanifolds of complex space forms $$\tilde M^{n}(4c)$$, $$n \geq 5$$, which satisfy the equality case of this inequality at every point.

### Most cited references11

• Record: found

### Some pinching and classification theorems for minimal submanifolds

(1993)
Bookmark
• Record: found

### On totally real submanifolds

(1974)
Bookmark
• Record: found

### Interaction of Legendre curves and Lagrangian submanifolds

(1997)
Bookmark

### Author and article information

###### Journal
2017-05-01
###### Article
1705.00685