Alexandrov Par Excellence.
Alexandrov spaces with nonnegative curvature outside a compact set.
Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes
We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized convex...
Algebraic analysis of the Rarita-Schwinger system in real dimension three
In this paper we use the explicit description of the Spin– Dirac operator in real dimension appeared in (Homma, Y., The Higher Spin Dirac Operators on –Dimensional Manifolds. Tokyo J. Math. 24 (2001), no. 2, 579–596.) to perform the algebraic analysis of the space of nullsolution of the system of equations given by several Rarita–Schwinger operators. We make use of the general theory provided by (Colombo, F., Sabadini, I., Sommen, F., Struppa, D. C., Analysis of Dirac systems and computational...
Algebraic aspects of web geometry
Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.
Algebraic characterization of the dimension of differential spaces
Algebraic geometry and local differential geometry
Algebraic Legendrian varieties [Book]
Algebraic properties of curvature operators in Lorentzian manifolds with large isometry groups.
Algebraic properties of the 3-state vector Potts model
Algebraic representation formulas for null curves in Sl(2,ℂ)
We study curves in Sl(2,ℂ) whose tangent vectors have vanishing length with respect to the biinvariant conformal metric induced by the Killing form, so-called null curves. We establish differential invariants of them that resemble infinitesimal arc length, curvature and torsion of ordinary curves in Euclidean 3-space. We discuss various differential-algebraic representation formulas for null curves. One of them, a modification of the Bianchi-Small formula, gives an Sl(2,ℂ)-equivariant bijection...
Algebraic restrictions on geometric realizations of curvature models
We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders,...
Algebraic theory of affine curvature tensors
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally appear in relative hypersurface theory.
Algebraically independent generators of invariant differential operators on a symmetric cone.
Algebras of integrals
Algèbres de Clifford dégénérées et revêtements des groupes conformes affines orthogonaux et symplectiques
Algèbres de Lie et groupes microlinéaires
Algèbres de Maurer-Cartan et Holonomie
Algèbres différentielles en théorie des champs
Les algèbres différentielles sont apparues comme des outils commodes ou même inévitables pour exprimer les symétries continues, exactes ou brisées, suivant la situation physique envisagée, dans le cadre de l’algorithme de Feynman de la théorie quantique des champs perturbative. Les algèbres de courants, les théories de Yang-Mills, la première quantification de la corde, sont proposées comme exemples classiques.
Algèbres et faisceaux d'algèbres de Lie graduées, associées à des espaces spinoriels et fibrations spinorielles par un principe de trialité