Results 1 to 10 of about 247 (35)
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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Singularities of generic line congruences [PDF]
Journal of the Mathematical Society of Japan, 2021 Line congruences are 2-dimensional families of lines in 3space. The singularities that appear in generic line congruences are folds, cusps and swallowtails ([7]). In this paper we give a geometric description of these singularities. The main tool used is
M. Craizer, Ronaldo Garcia
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Projective deformations of weakly orderable hyperbolic Coxeter orbifolds [PDF]
, 2012 A Coxeter n‐orbifold is an n‐dimensional orbifold based on a polytope with silvered boundary facets. Each pair of adjacent facets meet on a ridge of some order m, whose neighborhood is locally modeled on R n modulo the dihedral group of order 2m ...
Suhyoung Choi, Gye-Seon Lee
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Symmetric regularization, reduction and blow-up of the planar three-body problem [PDF]
, 2012 PROOFS - PAGE NUMBERS ARE TEMPORARY PACIFIC JOURNAL OF MATHEMATICS Vol. , No. , 2013 dx.doi.org/10.2140/pjm.2013..101 SYMMETRIC REGULARIZATION, REDUCTION AND BLOW-UP OF THE PLANAR THREE-BODY PROBLEM R ICHARD M OECKEL AND R ICHARD M ONTGOMERY We carry out
R. Moeckel, R. Montgomery
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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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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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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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