Related papers: Riemann normal coordinates, Fermi reference system…
Considering Riemannian submersions, we find necessary and sufficient conditions for when sub-Riemannian normal geodesics project to curves of constant first geodesic curvature or constant first and vanishing second geodesic curvatures. We…
Mass redistribution on Earth due to dynamic processes such as ice melting and sea level rise leads to a changing gravitational field, observable by geodetic techniques. Monitoring this change over time allows us to learn more about our…
The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the…
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…
In a family of compact, canonically polarized, complex manifolds equipped with K\"ahler-Einstein metrics the first variation of the lengths of closed geodesics was previously shown in by the authors in [arXiv:0808.3741v2] to be the geodesic…
In Theorem 1, we generalize the results of Szabo for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F. As an application we show…
The measurement of frequency shifts for light beams exchanged between two test masses nearly in free fall is at the heart of gravitational wave detection. It is envisaged that the derivative of the frequency shift is in fact limited by…
In this paper we analyze the local and global boundary rigidity problem for general Riemannian manifolds with boundary $(M,g)$. We show that the boundary distance function, i.e., $d_g|_{\partial M\times\partial M}$, known near a point $p\in…
General relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source described by the Kerr gravitational field. Specifically, observers that are spatially at rest in the exterior Kerr…
We give an explicit description of the Fefferman metric for twistor CR manifolds in terms of Riemannian structures on the base conformal 3-manifolds. As an application, we prove that chains and null chains on twistor CR manifolds project to…
The elements of the E\"otv\"os matrix are useful for various geodetic applications, such as the interpolation of the elements of the deflection of the vertical, the determination of gravity anomalies and the determination of geoid heights.…
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation…
The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we present an explicit form of the Riemannian metrics on…
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…
Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the…
We study deformations of the geodesic distances on a domain of R N induced by a function called conformal factor. We show that under a positive reach assumption on the domain (not necessarily a submanifold) and mild assumptions on the…
We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number…
The discrete wave equation in a multidimensional uniform space with local defects and sources is considered. The characterization of all possible defect configurations corresponding to given amplitudes of waves at the receivers (detectors)…
Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…
In this paper we define Fermi-type coordinates in a 2-dimensional Lorentz manifold, and use this coordinate system to provide a local characterization of constant Gaussian curvature metrics for such manifolds, following a classical result…