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arXiv · 2204.10538

Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds

Rika Akiyama·Takashi Sakai·Yuichiro Sato
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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.

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Rika Akiyama, Takashi Sakai, Yuichiro Sato. 2022-04-22. Variational problems for integral invariants of the second fundamental form of a map between pseudo-Riemannian manifolds. https://arxiv.org/abs/2204.10538

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