Smooth maps minimizing the energy and the calibrated geometry

2023/04/05 by Kota Hattori, Hattori, Kota
Mathematics · Physics and Astronomy · #53C38 #53C43 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2304.02788

openalex publication_date 2023/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the lower bound to the energy of smooth maps in the given homotopy class between Riemannian manifolds, and consider the energy functional which is minimized by the identity maps on the Riemannian manifolds with special holonomy groups.

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