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Related papers: Nearly Geodesic Riemannian Cubics in SO(3)

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We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\"uller space, this semisimplicity…

Geometric Topology · Mathematics 2025-04-24 Francisco Arana-Herrera , Alex Wright

Accurate quantification of complex human movements, such as gait, is essential for clinical diagnosis and rehabilitation but is often limited by traditional linear models rooted in Euclidean geometry. These frameworks frequently fail to…

Quantitative Methods · Quantitative Biology 2025-12-11 Tomáš Bůžek

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from…

Differential Geometry · Mathematics 2015-05-28 Mehmet Akif Akyol , Bayram Şahin

We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and find…

Differential Geometry · Mathematics 2010-11-03 Bayram Sahin

The purpose of this article is to introduce a new class of kernels on SO(3) for approximation and interpolation, and to estimate the approximation power of the associated spaces. The kernels we consider arise as linear combinations of…

Classical Analysis and ODEs · Mathematics 2011-06-14 Thomas Hangelbroek , Dominik Schmid

We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…

Metric Geometry · Mathematics 2021-01-06 Alexandru Chirvasitu

Given a connected Riemannian manifold $\mathcal{N}$, an \(m\)--dimensional Riemannian manifold $\mathcal{M}$ which is either compact or the Euclidean space, $p\in [1, +\infty)$ and $s\in (0,1]$, we establish, for the problems of…

Functional Analysis · Mathematics 2019-04-09 Antonin Monteil , Jean Van Schaftingen

Sets related to positively curved invariant Riemannian metrics on generalized Wallach spaces are considered. The problem arises in studying of the evolution of such metrics under the normalized Ricci flow equation. For Riemannian metrics of…

Differential Geometry · Mathematics 2024-03-05 Nurlan Abiev

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…

Differential Geometry · Mathematics 2016-09-06 Olga Gil-Medrano , Peter W. Michor , Martin Neuwirther

Let $M^{n}$ be an $n$-dimensional complete spacelike linear Weingarten submanifold immersed in a locally symmetric semi-Riemannian space $\mathbb{L}_{q}^{n+p}$ of index $q$, with parallel normalized mean curvature vector field and flat…

Differential Geometry · Mathematics 2026-02-17 Jogli G. S. Araújo , Weiller F. C. Barboza

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

Differential Geometry · Mathematics 2007-05-23 Michael T. Anderson

We study some Riemannian metrics on the space of regular smooth curves in the plane, viewed as the orbit space of maps from $S^1$ to the plane modulo the group of diffeomorphisms of $S^1$, acting as reparameterizations. In particular we…

Differential Geometry · Mathematics 2007-05-23 Peter W. Michor , David Mumford

Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to…

Machine Learning · Computer Science 2025-11-04 Chaoran Cheng , Yusong Wang , Yuxin Chen , Xiangxin Zhou , Nanning Zheng , Ge Liu

We investigate a generalization of cubic splines to Riemannian manifolds. Spline curves are defined as minimizers of the spline energy - a combination of the Riemannian path energy and the time integral of the squared covariant derivative…

Numerical Analysis · Mathematics 2017-11-17 Behrend Heeren , Martin Rumpf , Benedikt Wirth

Successful control of a rigid-body rotating in three dimensional space requires accurate estimation of its attitude. The attitude dynamics are highly nonlinear and are posed on the Special Orthogonal Group $SO(3)$. In addition, measurements…

Systems and Control · Electrical Eng. & Systems 2021-11-10 Hashim A. Hashim , Mohammed Abouheaf , Kyriakos G. Vamvoudakis

Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…

Optimization and Control · Mathematics 2025-04-09 Estefania Loayza-Romero , Kathrin Welker

Accurate rotation estimation is at the heart of robot perception tasks such as visual odometry and object pose estimation. Deep neural networks have provided a new way to perform these tasks, and the choice of rotation representation is an…

Computer Vision and Pattern Recognition · Computer Science 2021-01-19 Valentin Peretroukhin , Matthew Giamou , David M. Rosen , W. Nicholas Greene , Nicholas Roy , Jonathan Kelly

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…

Classical Analysis and ODEs · Mathematics 2015-03-17 T. Hangelbroek , F. J. Narcowich , J. D. Ward

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…

Optimization and Control · Mathematics 2022-09-29 Michael I. Jordan , Tianyi Lin , Emmanouil-Vasileios Vlatakis-Gkaragkounis

In this paper, we consider numerical characteristics of the connected compact Riemannian manifold (M, g) such as the supremum and infimum of the scalar curvature s, Ricci curvature Ric and sectional curvature sec, as well as their…

Differential Geometry · Mathematics 2025-05-22 Sergey Stepanov , Irina Tsyganok
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