We consider a length functional for C1 curves of fixed degree in graded manifolds equipped with a Riemannian metric. The first variation of this length functional can be computed only if the curve can be deformed in a suitable sense, and this condition is expressed via a differential equation along the curve. In the classical differential geometry setting, the analogous condition was considered by Bryant and Hsu in [7, 21], who proved that it is equivalent to the surjectivity of a holonomy map. The purpose of this paper is to extend this deformation theory to curves of fixed degree providing several examples and applications. In particular, we give a useful sufficient condition to guarantee the possibility of deforming a curve.

Citti G., Giovannardi G., Ritore M. (2022). VARIATIONAL FORMULAS FOR CURVES OF FIXED DEGREE. ADVANCES IN DIFFERENTIAL EQUATIONS, 27(5-6), 333-384 [10.57262/ade027-0506-333].

VARIATIONAL FORMULAS FOR CURVES OF FIXED DEGREE

Citti G.;
2022

Abstract

We consider a length functional for C1 curves of fixed degree in graded manifolds equipped with a Riemannian metric. The first variation of this length functional can be computed only if the curve can be deformed in a suitable sense, and this condition is expressed via a differential equation along the curve. In the classical differential geometry setting, the analogous condition was considered by Bryant and Hsu in [7, 21], who proved that it is equivalent to the surjectivity of a holonomy map. The purpose of this paper is to extend this deformation theory to curves of fixed degree providing several examples and applications. In particular, we give a useful sufficient condition to guarantee the possibility of deforming a curve.
2022
Citti G., Giovannardi G., Ritore M. (2022). VARIATIONAL FORMULAS FOR CURVES OF FIXED DEGREE. ADVANCES IN DIFFERENTIAL EQUATIONS, 27(5-6), 333-384 [10.57262/ade027-0506-333].
Citti G.; Giovannardi G.; Ritore M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/907712
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