Search results for "Geodesic"
showing 10 items of 131 documents
A comparison theorem for the first Dirichlet eigenvalue of a domain in a Kaehler submanifold
1994
AbstractWe give a sharp lower bound for the first eigenvalue of the Dirichlet eigenvalue problem on a domain of a complex submanifold of a Kaehler manifold with curvature bounded from above. The bound on the first eigenvalue is given as a function of the extrinsic outer radius and the bounds on the curvature, and it is attained only on geodesic spheres of a space of constant holomorphic sectional curvature embedded in the Kaehler manifold as a totally geodesic submanifold.
Rate of Mixing for the Geodesic Flow
2019
The main part of the chapter then consists in proving analogous bounds for the discrete-time and continuous-time geodesic ow for quotient spaces of simplicial and metric trees respectively.
Motzkin subposets and Motzkin geodesics in Tamari lattices
2014
The Tamari lattice of order n can be defined by the set D n of Dyck words endowed with the partial order relation induced by the well-known rotation transformation. In this paper, we study this rotation on the restricted set of Motzkin words. An upper semimodular join semilattice is obtained and a shortest path metric can be defined. We compute the corresponding distance between two Motzkin words in this structure. This distance can also be interpreted as the length of a geodesic between these Motzkin words in a Tamari lattice. So, a new upper bound is obtained for the classical rotation distance between two Motzkin words in a Tamari lattice. For some specific pairs of Motzkin words, this b…
Tensor tomography in periodic slabs
2018
Abstract The X-ray transform on the periodic slab [ 0 , 1 ] × T n , n ≥ 0 , has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless n = 0 . We characterize the kernel of the geodesic X-ray transform for L 2 -regular m -tensors for any m ≥ 0 . The characterization extends to more general manifolds, twisted slabs, including the Mobius strip as the simplest example.
A more distinctive representation for 3D shape descriptors using principal component analysis
2015
Many researchers have used the Heat Kernel Signature (or HKS) for characterizing points on non-rigid three-dimensional shapes and Classical Multidimensional Scaling (Classical MDS) method in object classification which we quote, in particular, the example of Jian Sun et al. (2009) [1]. However, in this paper, the main focuses on classification that we propose a concise and provably factorial method by invoking Principal Component Analysis (PCA) as a classifier to improve the scheme of 3D shape classification. To avoid losing or disordering information after extracting features from the mesh, PCA is used instead of the Classical MDS to discriminate-as much as possible-feature points for each…
Geodesics on spaces of almost hermitian structures
1994
A natural metric on the space of all almost hermitian structures on a given manifold is investigated.
Composite operators in asymptotic safety
2017
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dim…
Wormholes and nonsingular spacetimes in Palatinif(R)gravity
2015
We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric space-time, we find solutions which reduce to their Reissner-Nordstr\"om counterparts at large distances but undergo important non-perturbative modifications close to the center. Our new analysis reveals that the point-like singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular space-time, despite the existence of curvature divergences at the wormhole throat. …
Nonlinear σ -models in the Eddington-inspired Born-Infeld gravity
2020
In this paper we consider two different nonlinear $\sigma$-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though with important physical consequences. In particular, wormhole structures always arise, though this does not guarantee by itself the geodesic completeness of those space-times. In one of the models, quadratic in the canonical kinetic term, we identify a subset of solutions which are regular everywhere and are geodesically complete. We discuss characteristic features of these solutions and their dependence on the relationship between mass and global charge.
Nonsingular black holes, wormholes, and de Sitter cores from anisotropic fluids
2017
We study Born-Infeld gravity coupled to an anisotropic fluid in a static, spherically symmetric background. The free function characterizing the fluid is selected on the following grounds: i) recovery of the Reissner-Nordstr\"om solution of GR at large distances, ii) fulfillment of classical energy conditions and iii) inclusion of models of nonlinear electrodynamics as particular examples. Four branches of solutions are obtained, depending on the signs of two parameters on the gravity and matter sectors. On each branch, we discuss in detail the modifications on the innermost region of the corresponding solutions, which provides a plethora of configurations, including nonsingular black holes…