@misc{10481/70135,
year = {2021},
url = {http://hdl.handle.net/10481/70135},
abstract = {We consider in this paper an area functional defined on  submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this  area depends on the degree, not all variations are admissible. It turns out that the associated variational vector fields must satisfy a system of partial differential equations of first order on the submanifold. Moreover,  given a vector field solution of this system, we provide a sufficient condition that guarantees the possibility of deforming the original submanifold by variations preserving its degree. As in the case of singular curves in sub-Riemannian geometry, there are examples of isolated surfaces that cannot be deformed in any direction. When the deformability condition holds we compute the Euler-Lagrange equations. The resulting mean curvature operator can be of third order.},
organization = {Horizon 2020 Project ref. 777822: GHAIA},
organization = {MEC-Feder grants
MTM2017-84851-C2-1-P and PID2020-118180GB-I00},
organization = {Junta de Andalucía grants A-FQM-441-UGR18 and
P20-00164},
organization = {Research Unit MNat SOMM17/6109 and PRIN 2015 “Variational and perturbative aspects
of nonlinear differential problems”},
organization = {Universidad de Granada/CBUA},
keywords = {Sub-Riemannian manifolds},
keywords = {Graded manifolds},
keywords = {Degree of a submanifold},
keywords = {Admissible variations},
keywords = {Isolated submanifolds},
title = {Variational formulas for submanifolds of fixed degree},
author = {Citti, Giovanna and Giovannardi, Gianmarco and Ritoré Cortés, Manuel María},
}