We introduce variational obstacle avoidance problems on Riemannian manifolds and derive necessary conditions for the existence of their normal extremals. The problem consists of minimizing an energy ...

This is the official implementation of our paper "Riemannian Optimization on Relaxed Indicator Matrix Manifold" . We propose a fundamental manifold in machine learning—the Relaxed Indicator Matrix ...

ABSTRACT: In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3 . Under the assumptions ...

Existing operator learning methods mainly focus on regular computational domains, and have many components that rely on Euclidean structural data. However, many real-life operator learning problems ...

Let M be a Riemannian manifold with constant scalar curvature K which admits an infinitesimal conformal transformation. A necessary and sufficient condition in order that it be isometric with a sphere ...

An introduction to differentiable manifolds and Riemannian geometry by Boothby, William M. (William Munger), 1918- Publication date 1986 Topics Differentiable manifolds, Riemannian manifolds Publisher ...

Explore the representation of physical fields as Einstein manifolds and maximally symmetric spaces of constant scalar curvature. Discover the relationship between metric tensor and energy-momentum ...