Results 1 to 10 of about 425,594 (301)
Higher Order Connections [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
Michael G. Eastwood
doaj +9 more sources
Metric connections in projective differential geometry [PDF]
, 2008 We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations.
Michael Eastwood, Vladimir S. Matveev
core +8 more sources
INTEGRABLE SYSTEMS IN PROJECTIVE DIFFERENTIAL GEOMETRY
Kyushu Journal of Mathematics, 2000 Some of the most important classes of surfaces in projective 3-space are reviewed: these are isothermally asymptotic surfaces, projectively applicable surfaces, surfaces of Jonas, projectively minimal surfaces, etc. It is demonstrated that the corresponding projective "Gauss-Codazzi" equations reduce to integrable systems which are quite familiar from ...
E. V. Ferapontov
core +6 more sources
Benenti Tensors: A useful tool in Projective Differential Geometry [PDF]
Complex Manifolds, 2018 Two metrics are said to be projectively equivalent if they share the same geodesics (viewed as unparametrized curves). The degree of mobility of a metric g is the dimension of the space of the metrics projectively equivalent to g. For any pair of metrics
Manno Gianni, Vollmer Andreas
doaj +6 more sources
Differential geometry of Hilbert schemes of curves in a projective space [PDF]
Complex Manifolds, 2019 We describe the natural geometry of Hilbert schemes of curves in ℙ3and, in some cases, in ℙn, n ≥ 4.
Bielawski Roger, Peternell Carolin
doaj +5 more sources
Projective differential geometry of developable surfaces [PDF]
Transactions of the American Mathematical Society, 1913 Reprinted from the Transactions of the American Mathematical Society, v. 14. ; Vita. ; Thesis (Ph.D.)--University of Illinois, 1912. ; Mode of access: Internet.
William Wells Denton
openalex +3 more sources
Projective differential geometry of curved surfaces [PDF]
Transactions of the American Mathematical Society, 1907 The theory of surfaces, as developed by the author in the preceding three memoirs, was based upon the assumption that the surface considered was referred to its asymptotic curves. The complete system of invariants and covariallts was set up on that hypothesis.
E. J. Wilczynski
openalex +6 more sources
Differential Invariants of Conformal and Projective Surfaces [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We show that, for both the conformal and projective groups, all the differential invariants of a generic surface in three-dimensional space can be written as combinations of the invariant derivatives of a single differential invariant. The proof is based
Evelyne Hubert, Peter J. Olver
doaj +10 more sources
Differential geometry of complex projective plane conics [PDF]
Hokkaido Mathematical Journal, 2023 In this paper we study properties of complex plane projective curves from a geometric point of view. We focus our attention on properties of conics. We find that Gauss curvature determines a conic up to a hermitian transformation preserving the Fubini-Study metric of the complex projective plane and we discuss some other geometric properties of the ...
Enrique Artal Bartolo, R. MORÓN-SANZ
openalex +3 more sources
Metrics in projective differential geometry: the geometry of solutions to the metrizability equation [PDF]
The Journal of Geometric Analysis, 2018 27 pages.
Keegan J. Flood, A. Rod Gover
openalex +5 more sources