Results 61 to 70 of about 276,684 (327)
The Blaschke conjecture and great circle fibrations of spheres [PDF]
, 2003 We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.Comment: 61 pages, 8 ...
Benjamin Mckay, Benjamin Mckay
core +2 more sources
On Weingarten transformations of hyperbolic nets [PDF]
, 2013 Weingarten transformations which, by definition, preserve the asymptotic lines on smooth surfaces have been studied extensively in classical differential geometry and also play an important role in connection with the modern geometric theory of ...
Emanuel Huhnen-venedey +2 more
core +1 more source
Spinor calculus on 5-dimensional spacetimes [PDF]
, 2009 Penrose's spinor calculus of 4-dimensional Lorentzian geometry is extended to the case of 5-dimensional Lorentzian geometry. Such fruitful ideas in Penrose's spinor calculus as the spin covariant derivative, the curvature spinors or the definition of the
Alfonso García-Parrado Gómez-Lobo +8 more
core +4 more sources
Journal of High Energy Physics, 2020 Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces
Song He +3 more
doaj +1 more source
Feynman integrals in dimensional regularization and extensions of Calabi-Yau motives
Journal of High Energy Physics, 2022 We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the example of ...
Kilian Bönisch +4 more
doaj +1 more source
Noncommutative Differential Geometry of Generalized Weyl Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2016 Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed.
openaire +6 more sources
Scattering forms, worldsheet forms and amplitudes from subspaces
Journal of High Energy Physics, 2018 We present a general construction of two types of differential forms, based on any (n−3)-dimensional subspace in the kinematic space of n massless particles.
Song He +3 more
doaj +1 more source
Macaulay matrix for Feynman integrals: linear relations and intersection numbers
Journal of High Energy Physics, 2022 We elaborate on the connection between Gel’fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman Integrals.
Vsevolod Chestnov +6 more
doaj +1 more source
Examples of noncommutative manifolds: complex tori and spherical manifolds
, 2007 We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the differential geometry
Plazas, Jorge
core +2 more sources
Identifiability and numerical algebraic geometry
PLoS ONE, 2019 A common problem when analyzing models, such as mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given input-output data.
Daniel J. Bates +2 more
semanticscholar +1 more source