Related papers: Non-euclidean virtual reality II: explorations of …

Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…

We explore visual representations of tilings corresponding to Schl\"afli symbols. In three dimensions, we call these tilings "honeycombs". Schl\"afli symbols encode, in a very efficient way, regular tilings of spherical, euclidean and…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.

We investigate the singularities of two-ruled hypersurfaces in the Euclidean four-space. By considering the points that minimize the distance between adjacent rulings, we obtain a characterization the striction curve. We introduce the…

The complexity of the data generated by (magneto)-hydrodynamic (HD/MHD) simulations requires advanced tools for their analysis and visualization. The dramatic improvements in virtual reality (VR) technologies have inspired us to seek the…

In this note, we investigate the existence of smooth complete hypersurfaces in hyperbolic space with constant $(n-2)$-curvature and a prescribed asymptotic boundary at infinity. Previously, the existence was known only for a restricted…

We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.

3D-aware visual pretraining has proven effective in improving the performance of downstream robotic manipulation tasks. However, existing methods are constrained to Euclidean embedding spaces, whose flat geometry limits their ability to…

In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries,…

In this paper we review some author's results about Weingarten surfaces in Euclidean space $\r^3$ and hyperbolic space $\h^3$. We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property.…

In this paper, we describe the development and operating principles of an immersive virtual reality (VR) visualisation environment that is designed around the use of consumer VR headsets in an existing wide area motion capture suite. We…

Let X be an arbitrary hyperbolic geodesic metric space and let G be a countable non-elementary weakly acylindrical group of isometries of X. We show that the second bounded cohomology group of G with real coefficients or with coefficients…

We define virtual immersions, as a generalization of isometric immersions in a pseudo-Riemannian vector space. We show that virtual immersions possess a second fundamental form, which is in general not symmetric. We prove that a manifold…

Optical space in electromagnetic metamaterials may be engineered to emulate various exotic space-time geometries. However, these metamaterial models are limited in many respects. It is believed that real physical space-time strongly…

We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…

The main purpose is to describe the evolution of $\Xt = \Xs \wedge_- \Xss,$ with $\X(s,0)$ a regular polygonal curve with a nonzero torsion in the 3-dimensional hyperbolic space. Unlike in the Euclidean space, a nonzero torsion implies two…

Virtual reality (VR) enables data visualization in an immersive and engaging manner, and it can be used for creating ways to explore scientific data. Here, we use VR for visualization of 3D histology data, creating a novel interface for…

We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson's classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of…