Calibrated submanifolds with flat normal bundles
Differential Geometry
2025-08-21 v1
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.
Keywords
Cite
@article{arxiv.2508.14406,
title = {Calibrated submanifolds with flat normal bundles},
author = {W. Jacob Ogden},
journal= {arXiv preprint arXiv:2508.14406},
year = {2025}
}