By the same authors

From the same journal

From the same journal

Minimal Lagrangian submanifolds via the geodesic Gauss map

Research output: Contribution to journalArticlepeer-review



Publication details

JournalCommunications in Analysis and Geometry
DateAccepted/In press - 2 Sep 2015
DatePublished (current) - Dec 2016
Issue number5
Number of pages15
Original languageEnglish


For an oriented isometric immersed submanifold of the n-sphere, the spherical Gauss map is the Legendrian immersion of its unit normal bundle into the unit sphere subbundle of the tangent bundle of the sphere, and the geodesic Gauss map projects this into the manifold of oriented geodesics (the Grassmannian of oriented 2-planes in Euclidean n+1-space), giving a Lagrangian immersion of the unit normal bundle into a Kaehler-Einstein manifold. We give expressions for the mean curvature vectors for both the spherical and geodesic Gauss maps in terms of the second fundamental form of the immersion, and show that when it has conformal shape form this depends only on its mean curvature. In particular we deduce that the geodesic Gauss map of every minimal surface in the n-sphere is minimal Lagrangian. We also give simple proofs that: deformations of the immersion always correspond to Hamiltonian deformations of its geodesic Gauss map; the mean curvature vector of the geodesic Gauss map is always a Hamiltonian vector field. This extends work of Palmer on the case when the immersion is a hypersurface.

Bibliographical note

Date of Acceptance: 2/09/2015

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Discover related content

Find related publications, people, projects, datasets and more using interactive charts.

View graph of relations