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Geodesic Vectors and Flat Totally Geodesic Subalgebras in Nilpotent Metric Lie Algebras
We determine geodesics and flat totally geodesic subalgebras in higher-step nilpotent metric Lie algebras of dimension 5. It is surprising that in...
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On Geodesic Definiteness by Similarity Points
In this paper, we present some results obtained in the theory of geodesic map**s of surfaces. It is well known that a map** that is both...
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Generic density of geodesic nets
We prove that for a Baire-generic Riemannian metric on a closed smooth manifold, the union of the images of all stationary geodesic nets forms a...
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Approximation of the Geodesic Curvature and Applications for Spherical Geometric Subdivision Schemes
Many applications of geometry modelling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In...
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Geodesic Transformations of Distributions of Sub-Riemannian Manifolds
Let M be a sub-Riemannian contact-type manifold endowed with a distribution D . Using an endomorphism N : D → D of the distribution D , one can prolong...
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Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics
We show that a Kupka–Smale riemannian metric on a closed surface contains a finite primary set of closed geodesics, i.e. they intersect any other...
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Two-geodesic-transitive Graphs and Vertex-transitive Diameter Two Hexavalent Graphs
In this paper, we first investigate the family of vertex-transitive diameter 2 hexavalent graphs and particularly completely determine such graphs...
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Geodesic complexity for non-geodesic spaces
We define the notion of near-geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter’s notion of...
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A Curvature Inequality Characterizing Totally Geodesic Null Hypersurfaces
A well-known application of the Raychaudhuri equation shows that, under geodesic completeness, totally geodesic null hypersurfaces are unique which...
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Geodesic Currents
Geodesic currents play an essential role in the book. In this chapter we recall what they are and discuss their main properties. Something that might...
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The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space
The geometry of webs has been investigated over more than a century driven by still open problems. In our paper we contribute to extending the...
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Geodesic complexity via fibered decompositions of cut loci
The geodesic complexity of a Riemannian manifold is a numerical isometry invariant that is determined by the structure of its cut loci. In this...
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Geodesic Graphs for Geodesic Orbit Finsler \((\alpha ,\beta )\) Metrics on Spheres
The relation between Riemannian geodesic graphs and Finslerian geodesic graphs proved in a previous work is illustrated with explicit constructions....
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Some Rigidity Theorems for Anosov Geodesic Flows in Manifolds of Finite Volume
In this paper, we prove that if the geodesic flow of a complete manifold without conjugate points with sectional curvatures bounded below by
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Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds
Given a bounded symmetric domain Ω the author considers the geometry of its totally geodesic complex submanifolds S ⊂ Ω. In terms of the...
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The Structure of Geodesic Orbit Lorentz Nilmanifolds
The geodesic orbit property is useful and interesting in Riemannian geometry. It implies homogeneity and has important classes of Riemannian...