Search Results - "Fox, Daniel J. F"
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The commutative nonassociative algebra of metric curvature tensors
Published in Forum of mathematics. Sigma (01-01-2021)“…The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative…”
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Sectional nonassociativity of metrized algebras
Published in Annali di matematica pura ed applicata (01-04-2024)“…The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined analogously to the sectional curvature of a…”
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Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form
Published in Analysis and mathematical physics (01-03-2021)“…There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the…”
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Left-symmetric algebras and homogeneous improper affine spheres
Published in Annals of global analysis and geometry (01-04-2018)“…The nonzero level sets in n -dimensional flat affine space of a translationally homogeneous function are improper affine spheres if and only if the Hessian…”
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A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone
Published in Annali di matematica pura ed applicata (01-02-2015)“…This is an account of some aspects of the geometry of Kähler affine metrics based on considering them as smooth metric measure spaces and applying the…”
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Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero
Published in Mathematische Nachrichten (01-02-2017)“…Basic aspects of the equiaffine geometry of level sets are developed systematically. As an application there are constructed families of 2n‐dimensional…”
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Sectional nonassociativity of metrized algebras
Published 18-01-2024“…Annali di Matematica Pura ed Applicata, 2023 The sectional nonassociativity of a metrized (not necessarily associative or unital) algebra is defined…”
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Symmetries of the Space of Linear Symplectic Connections
Published in Symmetry, integrability and geometry, methods and applications (01-01-2017)“…There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic…”
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Conelike radiant structures
Published 11-09-2023“…Information Geometry, Vol. 6, No. 2 (2023) pp.463-595 Analogues of the classical affine-projective correspondence are developed in the context of statistical…”
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Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form
Published 12-05-2023“…Anal.Math.Phys. 11, 43 (2021) There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for…”
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Killing metrized commutative nonassociative algebras associated with Steiner triple systems
Published 18-05-2022“…Journal of Algebra. Vol. 608, No. 15 (2022), pp. 186-213 With each Steiner triple system there is associated a one-parameter family of commutative,…”
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Contact Projective Structures
Published in Indiana University mathematics journal (01-01-2005)“…A contact path geometry is a family of paths in a contact manifold each of which is everywhere tangent to the contact distribution and such that given a point…”
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The commutative nonassociative algebra of metric curvature tensors
Published 08-04-2021“…Forum of Mathematics, Sigma 9 (2021) e79 The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of…”
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Critical symplectic connections on surfaces
Published 02-01-2020“…J. Symplectic Geom. Vol. 17, No. 6 (2019), pp. 1683-1771 The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen…”
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Killing metrized commutative nonassociative algebras associated with Steiner triple systems
Published in Journal of algebra (15-10-2022)“…With each Steiner triple system there is associated a one-parameter family of commutative, nonassociative, nonunital algebras that are by construction exact,…”
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Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero
Published 03-11-2017“…Mathematische Nachrichten 290 (2017), no. 2-3, 293-320 Basic aspects of the equiaffine geometry of level sets are developed systematically. As an application…”
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Left-symmetric algebras and homogeneous improper affine spheres
Published 01-11-2017“…The nonzero level sets in $n$-dimensional flat affine space of a translationally homogeneous function are improper affine spheres if and only if the Hessian…”
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Conelike radiant structures
Published in Information geometry (01-11-2023)“…Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These…”
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Symmetries of the Space of Linear Symplectic Connections
Published 10-01-2017“…SIGMA 13 (2017), 002, 30 pages There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic…”
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