Calibrated submanifolds with flat normal bundles

Published 20 Aug 2025 in math.DG | (2508.14406v1)

Abstract: We show that submanifolds of Euclidean space which are calibrated by a constant-coefficient differential form and have flat normal bundles are planes. In fact, in a Riemannian manifold equipped with a parallel calibration, a calibrated submanifold subject to the condition that all shape operators commute is totally geodesic.

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Authors (1)

W. Jacob Ogden

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