Minimal real Kaehler submanifolds
S. Chion, M. Dajczer

TL;DR
This paper demonstrates that under certain generic conditions, Kaehler submanifolds immersed in Euclidean space with low codimension must be minimal, revealing a fundamental geometric property of such submanifolds.
Contribution
It establishes a new link between rank conditions on the second fundamental form and minimality for Kaehler submanifolds in low codimension.
Findings
Generic rank conditions imply minimality of the submanifold.
Existence of a one-parameter family of minimal immersions for simply connected cases.
Holomorphic submanifolds are exceptions to the minimality result.
Abstract
We show that generic rank conditions on the second fundamental form of an isometric immersion of a Kaehler manifold of complex dimension into Euclidean space with low codimension implies that the submanifold has to be minimal. If if simply connected, this amounts to the existence of a one-parameter associated family of isometric minimal immersions unless is holomorphic.
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 · Black Holes and Theoretical Physics
