On Jacobi fields and canonical connection in sub-Riemannian geometry [PDF]
, 2017 In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in ...
Barilari, Davide, Rizzi, Luca
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On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space
AIMS Mathematics, 2022 In Euclidean 3-space $ {\mathrm{E}}^3 $, a canonical subject is the focal surface of such a cliched space curve, which would be a two-dimensional corrosive with Lagrangian discontinuities. The tubular surfaces with respect to the B-Darboux frame and type-
Ibrahim AL-Dayel +2 more
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Non-commutative NLS-type hierarchies: dressing & solutions [PDF]
, 2019 We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation, and we ...
Doikou, Anastasia +2 more
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Equiaffine Darboux frames for codimension 2 submanifolds contained in hypersurfaces
Journal of the Mathematical Society of Japan, 2017 Consider a codimension $1$ submanifold $N^n\subset M^{n+1}$, where $M^{n+1}\subset\mathbb{R}^{n+2}$ is a hypersurface. The envelope of tangent spaces of $M$ along $N$ generalizes the concept of tangent developable surface of a surface along a curve. In this paper, we study the singularities of these envelopes.
CRAIZER, Marcos +2 more
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Lattice and q-difference Darboux-Zakharov-Manakov systems via $\bar{\partial}$-dressing method
, 1995 A general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of $\bar{\partial}$-dressing method .
B G Konopelchenko +23 more
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Special Smarandache Curves According To Darboux Frame In E3
, 2012 15 ...
BEKTAŞ, ÖZCAN, YÜCE, SALİM
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Dual Darboux Frame of a Timelike Ruled Surface and Darboux Approach to Mannheim Offsets of Timelike Ruled Surfaces [PDF]
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2013 12 ...
UĞURLU, HASAN HÜSEYİN, Onder, Mehmet
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Smarandache Curves of the Evolute Curve According to Sabban Frame
Communications in Advanced Mathematical Sciences, 2020 The aim of this paper is to define Smarandache curves according to the Sabban frame belonging to the unit Darboux vector of spherical indicatrix curve of the evolute curve. Also, we calculate the geodesic curvatures of these curves.
Süleyman Şenyurt, Yasin Altun
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$ C^* $-partner curves with modified adapted frame and their applications
AIMS Mathematics, 2023 In this study, the curve theory, which occupies a very important and wide place in differential geometry, has been studied. One of the most important known methods used to analyze a curve in differential geometry is the Frenet frame, which is a moving ...
Sezai Kızıltuǧ +3 more
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The Bianchi-Darboux transform of L-isothermic surfaces
, 2000 We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation.
Musso, E., Nicolodi, L.
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