Embedding into manifolds with torsion

TL;DR

This paper introduces a new class of geometries related to differential graded algebras, generalizing embedding results for real analytic manifolds into manifolds with special holonomy, with applications to hypersurfaces in specific geometric contexts.

Contribution

It extends known embedding theorems to a broader class of geometries involving torsion and differential graded algebras, including new results for hypersurfaces in nearly-Kaehler and alpha-Einstein-Sasaki manifolds.

Findings

Generalized embedding results for manifolds with special geometries

Proved existence of solutions for evolution equations in real analytic cases

Extended classical results to manifolds with torsion and differential graded algebra structures

Abstract

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfaces inside nearly-Kaehler and alpha-Einstein-Sasaki manifolds, proving that the corresponding evolution equations always admit a solution in the real analytic case.