Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds
Differential Geometry
2022-08-29 v2
Abstract
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae for integral invariants defined from invariant homogeneous polynomials of degree two. Among these integral invariants, we show that the Euler-Lagrange equation of the Chern-Federer energy functional is reduced to a second order PDE. Then we give some examples of Chern-Federer submanifolds in Riemannian space forms.
Keywords
Cite
@article{arxiv.2204.10538,
title = {Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds},
author = {Rika Akiyama and Takashi Sakai and Yuichiro Sato},
journal= {arXiv preprint arXiv:2204.10538},
year = {2022}
}
Comments
25 pages; a typo corrected in Remark 5.2; miscalculations corrected in Propositions 5.14, 5.16 and 5.17