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Metric connections in projective differential geometry [PDF]

open access: green, 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
A.R. Gover   +6 more
core   +9 more sources

Integrable systems in projective differential geometry [PDF]

open access: bronzeKyushu Journal of Mathematics, 1999
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.
Ferapontov, E. V.
core   +8 more sources

Benenti Tensors: A useful tool in Projective Differential Geometry [PDF]

open access: goldComplex 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   +7 more sources

Differential geometry of Hilbert schemes of curves in a projective space [PDF]

open access: goldComplex 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   +7 more sources

Projective differential geometry of curved surfaces [PDF]

open access: bronzeTransactions 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
semanticscholar   +7 more sources

Differential geometry of complex projective plane conics [PDF]

open access: greenHokkaido 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
semanticscholar   +4 more sources

Higher Order Connections [PDF]

open access: yesSymmetry, 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   +7 more sources

Equivalence problems in projective differential geometry [PDF]

open access: bronzeTransactions of the American Mathematical Society, 1984
Equivalence problems for abstract, and induced, projective structures are investigated. (i) The notion of induced projective structures on submanifolds of a projective space is rigorously defined. (ii) Equivalence problems for such structures are discussed; in particular, it is shown that nonplanar surfaces in R
Kichoon Yang
semanticscholar   +3 more sources

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