Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 55 for “"GEODESICS"”.
-
GEODESICS IN LORENTZIAN MANIFOLDS
<p>We present an extension of Geodesics in Lorentzian Manifolds (Semi-Riemannian Manifolds or pseudo-Riemannian Manifolds ). A geodesic on a Riemannian manifold is, locally, a length minimizing curve. On the other hand, geodesics in Lorentzian manifolds can be viewed as a distance between …
-
The evolution equation for closed magnetic geodesics
… field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for …
-
Frequencies of Bound Geodesics, Angle of Deflection For Null Geodesics In Kerr Space-Time, and Gravitational Anomalies In Gravastars.
… And we also extend our results to non-bound null geodesics, finding an exact result for the angle of deflection for equatorial trajectories. We also discuss a completely different problem. It is well known that there are very massive compact objects in the Universe. Despite some inconsistencies it …
-
Distribution of Holonomy about Closed Geodesics on Compact Hyperbolic 3-Manifolds
… compact hyperbolic 3-manifolds is their closed geodesics, which have both geometric and dynamical implications. These geodesics are parametrized by their length and holonomy, which describes the angle of rotation by parallel transport about the geodesic. First, we prove ambient prime geodesic …
-
An Analogue of the Laplace-Runge-Lenz Vector for Timelike Geodesics in Schwarzschild Spacetime
In Schwarzschild spacetime, the timelike geodesics are the trajectories of free, massive particles, orbiting a singularity at the origin r = 0. In this work we derive four scalar first integrals of timelike geodesics in Schwarzschild spacetime. Two of the first integrals, corresponding to energy …
-
Sugli spazi omogenei di dimensione tre SO(2) - isotropi
… C-V metrics. We determined the equations of the geodesics using the Killing vector fields and obtain explicitly the equation of the surface which con- tains the geodesics. After having determined the totally geodesics surfaces isometrically immersed in the C-V spaces, we studied the totally …
-
The broken non-abelian X-ray transform and inverse problems for connections at high fixed frequency
… by its parallel transports over a set of broken geodesics that start and end on the boundary. Here, a broken geodesic is a piecewise smooth curve formed by the composition of two geodesics that intersect transversally at a point. In Chapter 2, we consider the case where M = D\Ω is a causal …
-
ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ
… OF THE PRESENT THESIS IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A …
-
Conformal Properties of Spacetime
… was shown to fail in spacetimes which focus null geodesics. This is in contrast to our findings in asymptotically flat and asymptotically de Sitter spacetimes. Next we show how some of the methods established in the study of the Penrose property can be used to prove a version of the positive mass …
-
Geometric Methods for Point Estimation
… estimator. This estimator utilizes metric space geodesics to shrink an estimate towards a pre-specified, shrinkage point. It is shown that the performance of this geodesic James-Stein estimator depends on the curvature of the underlying metric space, where shrinkage is especially beneficial in …
-
Geometric and dynamical properties of Riemannian foliations
… metric, geometric and dynamical properties of geodesics orthogonal to the leaves of the foliation are studied.
-
A covariant approach to gravitational lensing
… this thesis is to study the properties of null geodesics in general relativistic models. This thesis is divided into two parts. In the first part, we introduce the (1+3)-covariant approach which will be used in our study of null geodesics and their applications to gravitational lensing. The …
-
Geometric Properties of the Ferrand Metric
… of a convex domain. We show that Ferrand geodesics are unique, that Ferrand balls are strictly Euclidean convex, and that Ferrand geodesics can be prolonged to Ferrand geodesic rays. Finally, we study the notion of a rolling disk condition and provide a sufficient geometric condition which …
-
Wave Equations on Curved Spacetimes
… where there are stably trapped null geodesics that have zero energy relative to an observer at infinity. We give a heuristic argument as to why this may lead to a non-linear instability, which can be seen at the linear level by studying the wave equation. We calculate the quasinormal …
-
Growth of Conjugacy Classes of Reciprocal Words in Triangle Groups
… G. The reciprocal words in G correspond to geodesics on O which pass through the order 2 cone point on O. We use methods from analytic combinatorics to count these words and to analyze the asymptotic behavior of their conjugacy classes with respect to the word length in the group for chosen …
-
Spectral geometry of hyperbolic 3-manifolds
… between quantities like volume, length of geodesics, area of embedded surfaces, isoperimetric constants, eigenvalues of the Laplacian, and Margulis numbers for hyperbolic 3-manifolds.
-
Gauge/Gravity Duality: Recovering the Bulk from the Boundary using AdS/CFT
… to the endpoints of boundary-to boundary null geodesics in the bulk spacetime) and the holographic entanglement entropy proposal (relating the entanglement entropy of certain subsystems on the boundary to the area of static minimal surfaces) to recover the bulk metric. Using null and …
-
The Asymptotic Cone of Teichmuller Space: Thickness and Divergence
… we characterize strongly contracting quasi-geodesics in Teichmüller space, generalizing results of Brock-Masur-Minsky. As a tool in the thesis, we develop a natural relative of the curve complex called the complex of separating multicurves which may be of independent interest. The final …
-
Homology products on Z2-quotients of free loop spaces of spheres
… information about geometrically distinct closed geodesics.
-
Riemannian Metric Learning via Optimal Transport
… between probability measures and compute geodesics on the manifold. We show that metrics learned using our method improve the quality of trajectory inference on scRNA and bird migration data at the cost of little additional cross-sectional data.
Page 1 of 3