Topology of phi-convex domains in calibrated manifolds

In [5], Harvey and Lawson showed that for any calibration phi there is an integer bound for the homotopy dimension of a strictly phi-convex domain and constructed a method to get these domains by using phi-free submanifolds. Here, we show how to get examples of phi-free submanifolds with different homotopy types for the quaternion calibration in H(n), associative calibration, and coassociative calibration in G(2) manifolds. Hence we give examples of strictly phi-convex domains with different homotopy types allowed by Morse Theory.


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Citation Formats
İ. Ünal, “Topology of phi-convex domains in calibrated manifolds,” BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, pp. 259–275, 2011, Accessed: 00, 2020. [Online]. Available: