Curvature invariants, Killing vector fields, connections and cohomogeneity

TL;DR

This paper introduces a bundle-theoretic approach to extend local isometries from curvature data, providing new proofs of classical and recent results in differential geometry.

Contribution

It develops a direct method for defining and extending local isometries using curvature invariants, simplifying proofs of key theorems.

Findings

New bundle-theoretic method for isometry extension

Conceptual proofs of Singer's classical result

Extension of recent results by the authors

Abstract

A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived.