المؤلفون: Annalisa Calini, Thomas Ivey, Emilio Musso

المساهمون: Calini, Annalisa, Ivey, Thoma, Musso, Emilio

مصطلحات موضوعية: mKdV, Legendrian curve, geometric flow, pseudohermitian CR geometry

الوصف: We investigate geometric evolution equations for Legendrian curves in the 3-sphere which are invariant under the action of the unitary group U(2). We define a natural symplectic structure on the space of Legendrian loops and show that the modified Korteweg-de Vries equation, along with its associated hierarchy, are realized as curvature evolutions induced by a sequence of Hamiltonian flows. For the flow among these that induces the mKdV equation, we investigate the geometry of solutions which evolve by rigid motions in U(2) Generalizations of our results to higher-order evolutions and curves in similar geometries are also discussed.

وصف الملف: ELETTRONICO

العلاقة: volume:20; issue:027; firstpage:1; lastpage:30; numberofpages:30; journal:SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS; https://hdl.handle.net/11583/2987569Test; https://www.emis.de/journals/SIGMATest/

الإتاحة: https://doi.org/10.3842/sigma.2024.027Test
https://hdl.handle.net/11583/2987569Test
https://www.emis.de/journals/SIGMATest/

المؤلفون: Emilio Musso

المصدر: Symmetry, Integrability and Geometry: Methods and Applications, Vol 8, p 030 (2012)

مصطلحات موضوعية: Mathematics, QA1-939

الوصف: The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave cnoidal solutions of the fifth-order Kaup-Kupershmidt equation are described.

وصف الملف: electronic resource

العلاقة: https://doaj.org/toc/1815-0659Test

الوصول الحر: https://doaj.org/article/2ef811dc91cc4c3ebca5e6cd22af2fa4Test

المؤلفون: Lorenzo Nicolodi, Emilio Musso

المصدر: Symmetry, Integrability and Geometry: Methods and Applications, Vol 5, p 067 (2009)

مصطلحات موضوعية: Lagrangian surfaces, affine symplectic geometry, moving frames, differential invariants, applicability, Mathematics, QA1-939

الوصف: We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.

وصف الملف: electronic resource

العلاقة: https://doaj.org/toc/1815-0659Test

الوصول الحر: https://doaj.org/article/c3ea9566c48f4fd8a3c4b3262b8622f9Test

المؤلفون: Emilio Musso, Lorenzo Nicolodi

المساهمون: Musso, Emilio, Nicolodi, Lorenzo

مصطلحات موضوعية: Complex conformal geometry, isotropic curve, complex symplectic group, projective structures on Riemann surface, meromorphic differentials on Riemann surface, minimal surface, CMC surface, flat front, W-curve, Goursat transformation

الوصف: Let Q3 be the complex 3-quadric endowed with its standard complex conformal structure. We study the complex conformal geometry of isotropic curves in Q3. By an isotropic curve, we mean a nonconstant holomorphic map from a Riemann surface into Q3, null with respect to the conformal structure of Q3. The relations between isotropic curves and a number of relevant classes of surfaces in Riemannian and Lorentzian spaceforms are discussed.

العلاقة: info:eu-repo/semantics/altIdentifier/wos/WOS:000836036000007; volume:33; issue:8; numberofpages:32; journal:INTERNATIONAL JOURNAL OF MATHEMATICS; https://hdl.handle.net/11381/2901334Test; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85132984742

الإتاحة: https://doi.org/10.1142/S0129167X22500549Test
https://hdl.handle.net/11381/2901334Test

المؤلفون: Emilio Musso

المساهمون: Musso, Emilio

مصطلحات موضوعية: Lorentz conformal geometry Timelike curve, Conformal timelike geodesics Einstein universe, Lorentz conformal compactification Conformal strain functional

الوصف: This paper studies the geometry of the critical points of the simplest conformally invariant variational problem for timelike curves in the n-dimensional Einstein universe. Such critical curves are referred to as conformal timelike geodesics. The functional defining the variational problem is the Lorentz analogue of the conformal arclength functional in Möbius geometry. We compute the Euler– Lagrange equations and show that the trajectory of a conformal timelike geodesic is constrained into some totally umbilical Einstein universe of dimension 2, 3, or 4. The case of dimension 2 leads to orbits of 1-parameter groups of Lorentz Möbius transformations, while that of dimension 3 has been dealt with in [8]. In this paper, we discuss the case of conformal timelike geodesics in the 4-dimensional Einstein universe whose trajectories are not contained in any lower dimensional totally umbilical Einstein universe. It is shown that such curves can be explicitly integrated by quadratures and explicit expressions in terms of elliptic functions and integrals are provided.

وصف الملف: STAMPA

العلاقة: info:eu-repo/semantics/altIdentifier/wos/WOS:000601091000027; volume:495; issue:2; firstpage:1124730; numberofpages:32; journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS; http://hdl.handle.net/11583/2854732Test; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85094956923; www.elsevier.com/locate/jmaa

الإتاحة: https://doi.org/10.1016/j.jmaa.2020.124730Test
http://hdl.handle.net/11583/2854732Test

المؤلفون: Francis E. Burstall, Emilio Musso, Mason Pember

المصدر: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :1507-1524

مصطلحات موضوعية: Holomorphic differentials, Mathematics - Differential Geometry, Surface (mathematics), Physics, 53A31, 53B25, 53C43, Mean curvature, Mathematical analysis, Harmonic map, Conformal map, Harmonic (mathematics), Codimension, Conformal Geometry, Theoretical Computer Science, Mathematics (miscellaneous), Differential Geometry (math.DG), Quartic function, Harmonic Maps, FOS: Mathematics, Congruence (manifolds), Mathematics::Differential Geometry, Harmonic Maps, Holomorphic differentials, Conformal Geometry

الوصف: 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, quasi-umbilical surfaces, constant mean curvature surfaces in 3-dimensional space forms or surfaces of constant lightlike mean curvature in 3-dimensional lightcones. We then investigate Bryant's quartic differential in this context and show that generically this is divergence free if and only if the surface under consideration is either superconformal or orthogonal to a harmonic congruence of codimension 2 spheres. We may then apply the previous result to characterise surfaces with such a property.
15 pages

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9593f4bd0bedb27e5f5d26616e0f660fTest
https://doi.org/10.2422/2036-2145.202007_112Test

المؤلفون: Emilio Musso, Lorenzo Nicolodi, and Filippo Salis

المساهمون: Musso, Emilio, Nicolodi, Lorenzo, Salis, Filippo

مصطلحات موضوعية: CR geometry of the 3-sphere, contact geometry, transversal curves, CR invariants of transversal knots, self-linking number, Bennequin number, the strain functional for transversal curves, critical knots

الوصف: Let S^3 be the unit 3-sphere with its standard Cauchy--Riemann (CR) structure induced from C^2. This paper investigates the CR geometry of curves in S^3 transversal to the contact distribution using the local CR invariants of S^3 thought of as a 3-dimensional CR manifold. More specifically, the focus is on the CR geometry of transversal knots in the 3-sphere. Four global invariants of transversal knots are considered: the phase anomaly, the pseudoconformal spin, the Maslov index, and the Cauchy--Riemann self-linking number. The relations between these invariants and the Bennequin number of a knot are discussed. Next, the simplest CR invariant variational problem for generic transversal curves, the CR strain functional, is considered and its closed critical curves are studied.

وصف الملف: ELETTRONICO

العلاقة: info:eu-repo/semantics/altIdentifier/wos/WOS:000590794800007; volume:16; issue:3; firstpage:312; lastpage:363; numberofpages:52; journal:ŽURNAL MATEMATIčESKOJ FIZIKI, ANALIZA, GEOMETRII; http://hdl.handle.net/11583/2849192Test; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-85094905251; https://jmage.ilt.kharkov.uaTest

الإتاحة: https://doi.org/10.15407/mag16.03.312Test
http://hdl.handle.net/11583/2849192Test
https://jmage.ilt.kharkov.uaTest

المؤلفون: Emilio Musso, Lorenzo Nicolodi

المساهمون: Musso, Emilio, Nicolodi, Lorenzo

مصطلحات موضوعية: CR 3-sphere, transversal curve, CR invariant, total CR twist, Griffiths' formalism, Lax formulation of E-L equation, integration by quadrature, closed critical curves

الوصف: We investigate the total CR twist functional on transversal curves in the standard CR 3-sphere S^3 in C^2. The question of the integration by quadratures of the critical curves and the problem of existence and properties of closed critical curves are addressed. A procedure for the explicit integration of general critical curves is provided and a characterization of closed curves within a speci c class of general critical curves is given. Experimental evidence of the existence of in nite countably many closed critical curves is provided.

العلاقة: volume:19; firstpage:1; lastpage:36; numberofpages:36; journal:SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS; https://hdl.handle.net/11381/2955572Test; https://www.emis.de/journals/SIGMATest/

الإتاحة: https://doi.org/10.3842/SIGMA.2023.101Test
https://hdl.handle.net/11381/2955572Test
https://www.emis.de/journals/SIGMATest/

المؤلفون: Emilio Musso, Álvaro Pámpano

مصطلحات موضوعية: Mathematics - Differential Geometry, Assicurare un’istruzione di qualità, equa ed inclusiva, Differential Geometry (math.DG), Applied Mathematics, equa ed inclusiva, FOS: Mathematics, Assicurare un’istruzione di qualità, Analysis

الوصف: 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 momentum. We prove that closed trajectories arise only when the momentum is a time-like vector. Indeed, for suitable values of the Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of countably many closed trajectories with time-like momentum, which depend on a pair of relatively prime natural numbers.

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e62ae231b0a6c2c17665f9040837dd79Test
https://hdl.handle.net/11583/2979220Test

المؤلفون: Emilio Musso, Álvaro Pámpano

المصدر: Journal of Nonlinear Science. 33

مصطلحات موضوعية: Mathematics - Differential Geometry, Differential Geometry (math.DG), Applied Mathematics, Modeling and Simulation, FOS: Mathematics, General Engineering, Bernoulli’s bending functionals · Closed trajectories · Critical curves · p-elastic curves

الوصف: 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 closed trajectories which depend on a pair of relatively prime natural numbers. A geometric description of these numbers and the relation with the shape of the corresponding critical trajectories is also given.
Comment: To appear in Journal of Nonlinear Science

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::702f230bf1edf05cd4447169848da208Test
https://doi.org/10.1007/s00332-022-09860-3Test