May/June 2022 Variational formulas for curves of fixed degree
Giovanna Citti, Gianmarco Giovannardi, Manuel Ritoré
Adv. Differential Equations 27(5/6): 333-384 (May/June 2022). DOI: 10.57262/ade027-0506-333

Abstract

We consider a length functional for $C^1$ 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.

Citation

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Giovanna Citti. Gianmarco Giovannardi. Manuel Ritoré. "Variational formulas for curves of fixed degree." Adv. Differential Equations 27 (5/6) 333 - 384, May/June 2022. https://doi.org/10.57262/ade027-0506-333

Information

Published: May/June 2022
First available in Project Euclid: 7 March 2022

Digital Object Identifier: 10.57262/ade027-0506-333

Subjects:
Primary: 49Q20 , 53C17

Rights: Copyright © 2022 Khayyam Publishing, Inc.

Vol.27 • No. 5/6 • May/June 2022
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