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arXiv · 2508.14406

Calibrated submanifolds with flat normal bundles

W. Jacob Ogden
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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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W. Jacob Ogden. 2025-08-20. Calibrated submanifolds with flat normal bundles. https://arxiv.org/abs/2508.14406

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