arXiv research

New findings show fundamental group is not audible in spherical space forms.

New curvature positivity helps classify spherical spaces and complex projective spaces.

In this paper we consider the spherical slant helices in $R^3$. More- over, we show how could be obtained to a spherical slant helix and we give some spherical slant helix examples in Euclidean 3-space.

Researchers find highest volumes for isospectral spherical orbifolds and space forms.

In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representatio…

In this paper, we give definitions and characterizations of normal and spherical curves in the dual space. We show that normal curves are also spherical curves in D^3.

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean $(n+1)-$space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces $\mathbb{E}^{3}$ and $$ respect…

Timelike geometry of spherical simplices is shown to be isometric to vector spaces.

The paper proves stability of inequalities for nearly spherical sets in various spaces.

Study local features of decorated representation spaces for spherical surfaces.

DELIMIT is a framework extension for deep learning in diffusion imaging, which extends the basic framework PyTorch towards spherical signals. Based on several novel layers, deep learning can be applied to spherical diffusion imaging data in a very convenient way. First, two spherical harmonic interpolation layers are a…

Study spherical convex bodies using $L_p$-floating areas and curvature entropy.

This paper is the second part of a study of the quantum free particle on spherical and hyperbolic spaces by making use of a curvature-dependent formalism. Here we study the analogues, on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($κ>0$) and $H_\k^3$ ($κ<0$), to the standard {\itshape spherical wav…

In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider some features of the forgetful map from the above moduli space of spherical sur…

Locally classifies 4D spherical symmetric Finsler spaces.

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

Study calculates eigenvalues and eigenfunctions for spherical triangles and finds fundamental gap behavior.

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems.

We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.

Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation t…

Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.

Dunkl connections on complex plane don't preserve metrics.

Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.

Simple geodesics on spherical tetrahedra identified for specific angles.

Study on evolutes and focal surfaces of pseudo-spherical framed immersions in anti-de Sitter space.

The study proves spherical polygon analogs of curve theorems, finding bounds on intersections and inflections.

Study degenerate Bianchi transformations for pseudo-spherical submanifolds in 5D space.

The study characterizes compact submanifolds with pinched Ricci curvature in Euclidean and spherical space forms.

In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indi…

In this paper, we show that small spherical soap bubbles in irreducible simply connected symmetric spaces of rank greater than one are constructed from the limits of a certain kind of modified mean curvature flows starting from small spheres in the Euclidean space of dimension equal to the rank of the symmetric space, …

The paper extends geometric inequalities for nearly spherical sets in various space forms.

Describes the space of spherical triangles on a smooth 3-manifold.

A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories, and in this case the vector spaces agree with the state spaces of the correspondi…

We study special functions on euclidean spaces from the viewpoint of riemannian symmetric spaces. Here the euclidean space $E^n = G/K$ where $G$ is the semidirect product $R^n \cdot K$ of the translation group with a closed subgroup $K$ of the orthogonal group O(n). We give exact parameterizations of the space of $(G,K…

We prove that orientable index one minimal surfaces in spherical space forms with large fundamental group have genus at most two. This confirms a conjecture of R. Schoen for an infinite class of 3-manifolds.

Researchers found new functions for spherical clothoids using special functions.

The paper classifies equivariant test configurations for spherical varieties.

Study $Θ$-invariants for spherical 3-manifolds via $\mathbb{Z}π$-homology equivalences.

In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its …

Study spherically symmetric Finsler metrics with specific curvature properties.

Proves equality in Minkowski inequality for static, flat manifolds.

Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a survey of some of the main results and a guide to the literature.

New flow for capillary surfaces converges to spherical caps.

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a…

In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of $\mathrm{SO}(4)$, this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3…

Study shows spherical embedding and immersion components are related to homotopy groups.

Spherical quadrilaterals classified based on geometric properties.

Two subset germs of Euclidean spaces are called blow-spherically equivalent, if their spherical modifications are homeomorphic and the homeomorphism induces homeomorphic tangent links. Blow-spherical equivalence is stronger than the topological equivalence but weaker than the Lipschitz equivalence. We introduce the thi…