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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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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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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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A System of Hamilton-Jacobi Equations Characterizing Geodesic Centroidal Tessellations
We introduce a class of systems of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e., tessellations of domains with...
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Evolution of eigenvalue of the Wentzell-Laplace operator along the geodesic curvature flow
In this paper, we study continuity, differentiability and monotonicity for the first nonzero eigenvalue of the Wentzell-Laplace operator along the...
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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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Fully Nonlinear Equations of Krylov Type on Riemannian Manifolds with Totally Geodesic Boundary
In this paper, we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic...
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Integrability of a Geodesic Flow on the Intersection of Several Confocal Quadrics
AbstractThe classical Jacobi–Chasles theorem states that tangent lines drawn at all points of a geodesic curve on a quadric in n -dimensional...
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Winding of geodesic rays chosen by a harmonic measure
We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain...
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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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Invariants of Geodesic, Potential, and Dissipative Systems with Three Degrees of Freedom
AbstractTensor invariants (first integrals and differential forms) of homogeneous dynamical systems on the tangent bundles of smooth...
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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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Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves
We investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we...
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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...
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Metric structures that admit totally geodesic foliations
Motivated by the problem of finding suitable structures on a manifold M to obtain totally geodesic foliations, we recently introduced the weakened...
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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...
