A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper defines embolic volume and relates it to Betti number using the covering trick.
Extreme black holes with $\SU(2)$ symmetry have a specific near horizon geometry.
Study of harmonic Riemannian submersions from 3D geometries.
We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in , and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.
Classification of constant curvature surfaces in Berger spheres.
Minimal equators and homological systoles found in Berger projective spaces.
The paper explores geometric decompositions for Ricci tensors and their applications.
Study non-minimal surfaces in homogeneous 3-manifolds with constant mean curvature.
The paper classifies biharmonic immersions and submersions in specific spheres.
Study shows magnetic trajectories in Berger spheres are homogeneous.
In this paper, we give a survey of various sphere theorems in geometry. These include the topological sphere theorem of Berger and Klingenberg as well as the differentiable version obtained by the authors. These theorems employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton'…
In this paper we will investigate the global properties of complete Hilbert manifolds with upper and lower bounded sectional curvature. We shall prove the Focal Index Lemma that we will allow us to extend some classical results of finite dimensional Riemannian geometry such as Rauch and Berger Theorems and the Topogono…
The invariant metric affine connections on Berger spheres which are Einstein with skew torsion are determined in both Riemannian and Lorentzian signature. Expressions of such connections are explicitly given. In particular, every Berger sphere with Lorentzian signature admits invariant metric affine connections Einstei…
The subgroups of GL(n,R) that act irreducibly on R^n and that can occur as the holonomy of a torsion-free affine connection on an n-manifold are classified, thus completing the work on this subject begun by M. Berger in the 1950s. The methods employed include representation theory, the theory of hermitian symmetric spa…
Study geodesics on a modified cotangent bundle over Kählerian manifolds.
New symmetric Willmore tori emerge from Clifford torus in Berger spheres.
Irreducible skew-Berger algebras $\g\subset\gl(n,\Co)$, i.e. algebras spanned by the images of the linear maps $R:\odot^2\Co^n\to\g$ satisfying the Bianchi identity, are classified. These Lie algebras can be interpreted as irreducible complex Berger superalgebras contained in $\gl(0|n,\Co)$.
We characterize helix surfaces in the Berger sphere, that is surfaces which form a constant angle with the Hopf vector field. In particular, we show that, locally, a helix surface is determined by a suitable 1-parameter family of isometries of the Berger sphere and by a geodesic of a 2-torus in the 3-dimensional sphere…
In the 1-parameter family of Berger spheres S^3(a), a > 0 (S^3(1) is the round 3-sphere of radius 1) we classify the stable constant mean curvature spheres, showing that in some Berger spheres (a close to 0) there are unstable constant mean curvature spheres. Also, we classify the orientable compact stable constant mea…
Numerical discovery matches eta invariant on Berger spheres with conformal anomaly on round spheres.
The study of stable and index compact minimal submanifolds in Berger spheres.
We construct compact arbitrary Euler characteristic orientable and non-orientable minimal surfaces in the Berger spheres. Besides we show an interesting family of surfaces that are minimal in every Berger sphere, characterizing them by this property. Finally we construct, via the Daniel correspondence, new examples of …
Study on new metrics on para-Kähler-Norden manifolds with conformal deformation.
The study classifies surfaces in Berger spheres as Willmore and Hopf tori.
Study of associative submanifolds in Berger space SO(5)/SO(3).
Study harmonicity on tangent bundles with a specific metric.
A classical result due to Blaschke states that for every analytic self-map of the open unit disk of the complex plane there exists a Blaschke product such that the zero sets of and agree. In this paper we show that there is an analogue statement for critical sets, i.e. for every analytic self-map of…
We compute the Eells-Kuiper invariant of the Berger manifold SO(5)/SO(3) and determine that it is diffeomorphic to the total space of an S^3-bundle over S^4. This answers a question raised by K. Grove and W. Ziller.
The paper studies stability and instability of minimal submanifolds in complex Einstein spaces.
A conjecture of Berger states that, for any simply connected Riemannian manifold all of whose geodesics are closed, all prime geodesics have the same length. We firstly show that the energy function on the free loop space of such a manifold is a perfect Morse-Bott function with respect to a suitable cohomology. Secondl…
New Finsler flow on 2-torus has chaotic dynamics.
We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Weiß, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, for special cases, we prove that the volume-normalized standard 3-sp…
Classifies totally geodesic submanifolds in Hopf-Berger spheres.
In 1955, Berger \cite{Ber} gave a list of irreducible reductive representations which can occur as the holonomy of a torsion-free affine connection. This list was stated to be complete up to possibly a finite number of missing entries. In this paper, we show that there is, in fact, an infinite family of representations…
New proof confirms flat equilateral torus is λ1-maximal.
The integral of the top dimensional term of the multiplicative sequence of Pontryagin forms associated to an even formal power series is calculated for special Riemannian metrics on the unit ball of a hermitean vector space. Using this result we calculate the generating function of the reduced Dirac and signature eta-i…
Our aim in this paper is to investigate some geometrical properties of Berger Spheres i.e. homogeneous Ricci solitons and harmonicity properties of invariant vector fields. We determine all vector fields which are critical points for the energy functional restricted to vector fields. We also see that do not exist any v…
Helix surfaces in Anti-de Sitter space maintain constant Gaussian curvature.
Study 3-Sasakian and G2 structures on manifolds.
We show that the group of smooth isometries of a complemented sub-Riemannian manifold form a Lie group and establish dimension estimates based on the torsion of the canonical connection. We explore the interaction of curvature and the structure of isometries and Killing fields and derive a Bochner formula for Killing f…
We give an exhaustive description of all simply connected odd dimensional cohomogeneity one manifolds that can possibly support an invariant metric with positive sectional curvature. Among the known examples of odd dimensional manifolds with positive curvature, apart from spheres, there are two infinite families among …
The minimal area of Finsler disks with minimizing geodesics is at least 6/π r^2.
The aim of this article is to present a comparative review of Riemannian and Finsler geometry. The structures of cut and conjugate loci on Riemannian manifolds have been discussed by many geometers including H. Busemann, M. Berger and W. Klingenberg. The key point in the study of Finsler manifolds is the non-symmetric …
Ricci flow can change metrics with positive curvature to those without.
We classify constant mean curvature surfaces invariant by a 1-parameter group of isometries in the Berger spheres and in the special linear group Sl(2, R). In particular, all constant mean curvature spheres in those spaces are described explicitly, proving that they are not always embedded. Besides new examples of Dela…
The volume spectrum of fiber bundles is bounded by the product of the base's volume spectrum and the fiber's volume.
Inequalities for Riemannian manifolds with upper sectional curvature bounds.
In this work, we study the stability of Hopf vector fields on Lorentzian Berger spheres as critical points of the energy, the volume and the generalized energy. In order to do so, we construct a family of vector fields using the simultaneous eigenfunctions of the Laplacian and of the vertical Laplacian of the sphere. T…