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Publications [#302469] of Colleen M Robles

Papers Published

  1. Robles, C, Parallel calibrations and minimal submanifolds, Illinois Journal of Mathematics, vol. 56 no. 2 (December, 2012), pp. 383-395, ISSN 0019-2082
    (last updated on 2018/11/18)

    Given a parallel calibration φ ∈ Ω p (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⊂Ω p (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 G 2 -manifolds, and the Cayley calibration on Spin(7)-manifolds.) © 2013 University of Illinois.
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