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.
Study on qc geometry of spherical qc manifolds and their convex cocompact subgroups.
Solution to qc Yamabe problem on non-spherical quaternionic contact manifolds.
We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity assumption and for torsion-free fundamental groups they are still diff…
Quaternionic contact heat equation studied on compact manifolds.
QC-SPHARM detects Alzheimer's Disease early using hippocampal surface geometry.
Study shows non-umbilical qc hypersurfaces in hyper-Kähler manifolds have specific structures.
We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space $\Hnn$ and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in $\Hnn$ is contained in one of the three qc-hyperquadrics in $\Hnn$. Moreover, we show tha…
Study on quaternionic contact structures with integrable complementary distribution.
We prove a quaternionic contact versions of the Obata's sphere theorems. We show that if the first positive eigenvalue of the sub-Laplacian on a compact qc manifold of dimension bigger than seven takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard…
The paper establishes sub-gradient estimates and entropy formulas for quaternionic contact geometry heat equations.
The main result is that the qc-scalar curvature of a seven dimensional quaternionic contact Einstein manifold is a constant. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local structure equations. Finally, regular qc-Ricci flat structures are shown to fibre…
A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension as well as on the quaternionic Heisenberg group is given. A uniqueness theorem for the qc Yamabe problem in a compact locally 3-Sasakian manifold is shown.
Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…
The paper proves new curvature estimates in quaternionic contact geometry.
In this note, we prove that the CR manifold which is induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard.
On 7D quaternionic contact manifolds, eigenvalue bounds imply special structure.
We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely …
We investigate the Fefferman spaces of conformal type which are induced, via parabolic geometry, by the quaternionic contact (qc) manifolds introduced by O.Biquard. Equivalent characterizations of these spaces are proved: as conformal manifolds with symplectic conformal holonomy of the appropriate signature; as pseudo-…
We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of Carnot-Carathéodory metric in the conformal class. The result of this computation has appli…
We investigate quaternionic contact (qc) manifolds from the point of view of intrinsic torsion. We argue that the natural structure group for this geometry is a non-compact Lie group K containing Sp(n)H^*, and show that any qc structure gives rise to a canonical K-structure with constant intrinsic torsion, except in se…
Develops QC theory for 3D point clouds, extending existing algorithms.
QC-ST and CoCo methods correct batch effects in metabolomics data.
Study heat kernel on quaternionic contact manifolds, finding linear dependence of coefficients on curvature.
We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution. We prove a general Myers theorem and establish a Cartan-Hadamard result for almost qc-Einstein manifolds.
We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional…
The 'anholonomic frame' method (see gr-qc/0005025, gr-qc/0001060 and hep-th/0110250) is applied for constructing new classes of exact solutions of vacuum Einstein equations with off-diagonal metrics in 4D and 5D gravity. We examine several black tori solutions generated by anholonomic transforms with non-trivial topolo…
We show that the fundamental 4-form on a quaternionic contact manifold of dimension at least eleven is closed if and only if the torsion endomorphism of the Biquard connection vanishes. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-Sasakian structures.
Quaternion Conformer GAN (QC-GAN) is a parameter-efficient speech enhancement framework that combines a Quaternion Conformer generator with MetricGAN-based training.
New knots not rationally concordant to their reverses found.
In this paper we establish an analogue of the classical Lichnerowicz' theorem giving a sharp lower bound of the first non-zero eigenvalue of the sub-Laplacian on a compact seven-dimensional quaternionic contact manifold, assuming a lower bound of the qc-Ricci tensor, torsion tensor and its distinguished covariant deriv…
Quantum computing improves fault diagnosis in industrial processes.
Unified AI system for data quality control and governance in regulated environments.
Hybrid QC system for Bengali questions using smart data balancing.
A version of Lichnerowicz' theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(1)Sp(1) component of the qc-Ricci curvature on a compact seven dimensional quaternionic contact manifold is established. It is shown that in the case of a seven dimensional compact 3-Sasakian ma…
A novel density-based approach QC detects outliers in data with high precision.
In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries and local anisotropy and define certain generalizations of manifolds with Killing …
This paper analyzes convergence of DP-SGD with adaptive quantile clipping.
Study on spherical CR manifolds with non-trivial Chern classes.
We prove that the groups of orientation preserving quasiconformal or bilipschitz homeomorphisms of S^n are simple in dimensions 2 and higher.
Classifies involutions on spherical 3-manifolds.
QC methods improve reliability of machine learning-based image segmentation.
We report on some aspects and recent progress in certain problems in the sub-Riemannian CR and quaternionic contact (QC) geometries. The focus are the corresponding Yamabe problems on the round spheres, the Lichnerowicz-Obata first eigenvalue estimates, and the relation between these two problems. A motivation from the…
Researchers find Fenchel-Nielsen coordinates for asymptotically conformal maps on hyperbolic surfaces.
A novel method automates quality control of fMRI scans, improving accuracy and generalizability.
Kähler-Ricci flow on spherical Fano manifolds converges to a soliton.
New theorem shows nearly spherical manifolds can be mapped from spheres.
The paper compares spectral geometry in hyperbolic and spherical manifolds.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.