Math @ Duke
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Publications [#302469] of Colleen M Robles
Papers Published
- Robles, C, Parallel calibrations and minimal submanifolds,
Illinois Journal of Mathematics, vol. 56 no. 2
(January, 2012),
pp. 383-395, ISSN 0019-2082 [doi]
(last updated on 2024/03/28)
Abstract: 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.
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