Zobrazeno 1 - 10
of 227
pro vyhledávání: '"Musso, Emilio"'
The paper focuses on the conformal Lorentz geometry of quasi-umbilical timelike surfaces in the $(1+2)$-Einstein universe, the conformal compactification of Minkowski 3-space realized as the space of oriented null lines through the origin of $\mathbb
Externí odkaz:
http://arxiv.org/abs/2410.10330
Autor:
Musso, Emilio, Pampano, Alvaro
We provide a geometric transformation on null curves in the anti-de Sitter $3$-space (AdS) which induces the B\"{a}cklund transformation for the KdV equation. In addition, we show that this geometric transformation satisfies a suitable permutability
Externí odkaz:
http://arxiv.org/abs/2312.10765
Autor:
Musso, Emilio, Pampano, Alvaro
We formulate integrable flows related to the KdV hierarchy on null curves in the anti-de Sitter 3-space (${\rm AdS}$). Exploiting the specific properties of the geometry of ${\rm AdS}$, we analyze their interrelationships with Pinkall flows in centro
Externí odkaz:
http://arxiv.org/abs/2311.11137
Publikováno v:
SIGMA 20 (2024), 027, 30 pages
We investigate geometric evolution equations for Legendrian curves in the 3-sphere which are invariant under the action of the unitary group ${\rm U}(2)$. We define a natural symplectic structure on the space of Legendrian loops and show that the mod
Externí odkaz:
http://arxiv.org/abs/2308.10125
Autor:
Musso, Emilio, Nicolodi, Lorenzo
Publikováno v:
SIGMA 19 (2023), 101, 36 pages
We investigate the total CR twist functional on transversal curves in the standard CR 3-sphere $\mathrm S^3 \subset \mathbb C^2$. The question of the integration by quadratures of the critical curves and the problem of existence and properties of clo
Externí odkaz:
http://arxiv.org/abs/2307.04763
Autor:
Musso, Emilio, Pampano, Alvaro
We study critical trajectories in the hyperbolic plane for the $1/2$-Bernoulli's bending energy with length constraint. Critical trajectories with periodic curvature are classified into three different types according to the causal character of their
Externí odkaz:
http://arxiv.org/abs/2302.03378
Autor:
Musso, Emilio, Pampano, Alvaro
We study critical trajectories in the sphere for the $1/2$-Bernoulli's bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of infinitely many clo
Externí odkaz:
http://arxiv.org/abs/2204.01096
Autor:
Musso, Emilio, Nicolodi, Lorenzo
Let $\mathbb{Q}_3$ be the complex 3-quadric endowed with its standard complex conformal structure. We study the complex conformal geometry of isotropic curves in $\mathbb{Q}_3$. By an isotropic curve we mean a nonconstant holomorphic map from a Riema
Externí odkaz:
http://arxiv.org/abs/2110.02838
Publikováno v:
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXIII (2022), 1507-1524
We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the orthogonal surfaces of such congruences as either $S$-Willmore surfaces,
Externí odkaz:
http://arxiv.org/abs/2007.03992
Publikováno v:
Zh. Mat. Fiz. Anal. Geom. 16 (2020), no. 3, 312-363
Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy-Riemann (CR) structure. This paper investigates the CR geometry of curves in $\mathrm S^3$ which are transversal to the contact distribution, using the local CR invariants
Externí odkaz:
http://arxiv.org/abs/2004.11350