Math @ Duke

Publications [#302469] of Colleen M Robles
Papers Published
 Robles, C, Parallel calibrations and minimal submanifolds,
Illinois Journal of Mathematics, vol. 56 no. 2
(December, 2012),
pp. 383395, ISSN 00192082
(last updated on 2018/02/22)
Abstract: Given a parallel calibration φ ∈ Ω p (M) on a Riemannian manifold M, I prove that the φcritical submanifolds with nonzero critical value are minimal submanifolds. I also show that the φcritical 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 CalabiYau manifolds, (co)associative calibrations on G 2 manifolds, and the Cayley calibration on Spin(7)manifolds.) © 2013 University of Illinois.


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