Results 1 to 10 of about 226 (24)
Differential geometry of grassmannians and the Plücker map [PDF]
Open Mathematics, 2012 Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were ...
Anan’in Sasha, Grossi Carlos
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Discrete Laplace cycles of period four
Open Mathematics, 2012 We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation ...
Schröcker Hans-Peter
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Hilbert geometry of polytopes [PDF]
, 2009 It is shown that the Hilbert metric on the interior of a convex polytope is bilipschitz to a normed vector space of the same dimension.Comment: 11 pages, minor changes, to appear in Archiv ...
Bernig, Andreas
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Benenti Tensors: A useful tool in Projective Differential Geometry
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
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On a Class of Two-Dimensional Douglas and Projectively Flat Finsler Metrics [PDF]
, 2013 In this paper, we study a class of two-dimensional Finsler metrics defined by a Riemannian metric $\alpha$ and a 1-form $\beta$. We characterize those metrics which are Douglasian or locally projectively flat by some equations.
Yang, Guojun
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, 2015 We prove that the general fibre of the $i$-th Gauss map has dimension $m$ if and only if at the general point the $(i+1)$-th fundamental form consists of cones with vertex a fixed $\mathbb P^{m-1}$, extending a known theorem for the usual Gauss map.
De Poi, Pietro, Ilardi, Giovanna
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Differential Invariants of Conformal and Projective Surfaces [PDF]
, 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
Hubert, Evelyne, Olver, Peter J.
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Binary differential equations at parabolic and umbilical points for $2$-parameter families of surfaces [PDF]
, 2017 We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic $2$-parameter families of surfaces in $\mathbb P^3$ by comparing our projective classification of Monge forms ...
Kabata, Yutaro +2 more
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Some calibrated surfaces in manifolds with density
, 2010 Hyperplanes, hyperspheres and hypercylinders in $\Bbb R^n$ with suitable densities are proved to be weighted minimizing by a calibration argument. Also calibration method is used to prove a weighted minimal hypersurface is weighted area-minimizing ...
Barbosa +17 more
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Metric connections in projective differential geometry
, 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
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