Parallel calibrations and minimal submanifolds

Journal Article (Journal Article)

Given a parallel calibration φ ∈ Ωp(M) on a Riemannian manifold M, I prove that the φ-critical submanifolds with nonzero critical value are minimal submanifolds. I also show that the φ-critical submanifolds are precisely the integral manifolds of a C∞(M)-linear subspace P⊂Ωp(M). In particular, the calibrated submanifolds are necessarily integral submanifolds of the system. (Examples of parallel calibrations include the special Lagrangian calibration on Calabi-Yau manifolds, (co)associative calibrations on G2-manifolds, and the Cayley calibration on Spin(7)-manifolds.) © 2013 University of Illinois.

Full Text

Duke Authors

Cited Authors

  • Robles, C

Published Date

  • January 1, 2012

Published In

Volume / Issue

  • 56 / 2

Start / End Page

  • 383 - 395

International Standard Serial Number (ISSN)

  • 0019-2082

Digital Object Identifier (DOI)

  • 10.1215/ijm/1385129954

Citation Source

  • Scopus