Complete Riemannian $G_2$ Holonomy Metrics on Deformations of Cones over $S^3\times S^3$

TL;DR

This paper constructs complete Riemannian metrics with $G_2$ holonomy on manifolds derived from deformations of cones over $S^3 imes S^3$, advancing understanding of special holonomy spaces.

Contribution

It provides explicit constructions of complete $G_2$ holonomy metrics on deformed cone manifolds over $S^3 imes S^3$, expanding known examples.

Findings

Explicit $G_2$ metrics on deformed cones over $S^3 imes S^3$

Demonstrates completeness of the constructed metrics

Advances the classification of $G_2$ holonomy spaces

Abstract

Complete Riemannian metrics with holonomy group $G_2$ are constructed on the manifolds obtained by deformations of cones over $S^3 \times S^3$.