Generalizes Chern-Lashof theorem to admissible compact frontals, proving total absolute curvature >= sum of Betti numbers, with equality (total=2, first-kind singularities) implying image is closed convex domain in affine n-subspace.
Koike, Theorems of Gauss-Bonnet and Chern-Lashof types in a simply connected sym- metric space of non-positive curvature , Tokyo J
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The total absolute curvature of submanifolds with singularities
Generalizes Chern-Lashof theorem to admissible compact frontals, proving total absolute curvature >= sum of Betti numbers, with equality (total=2, first-kind singularities) implying image is closed convex domain in affine n-subspace.