Abstract
In [5], Harvey and Lawson showed that for any calibration ϕ there is an integer bound for the homotopy dimension of a strictly ϕ-convex domain and constructed a method to get these domains by using ϕ-free submanifolds. Here, we show how to get examples of ϕ-free submanifolds with different homotopy types for the quaternion calibration in ℍn, associative calibration, and coassociative calibration in G2 manifolds. Hence we give examples of strictly ϕ-convex domains with different homotopy types allowed by Morse Theory.
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