Duality in a special class of submanifolds and Frobenius manifolds

TL;DR

This paper introduces a duality principle for a specific class of submanifolds in pseudo-Euclidean spaces with potential normals, and demonstrates that any Frobenius manifold can be embedded as a flat submanifold within this class.

Contribution

It defines a new class of submanifolds with potential normals and establishes a connection to Frobenius manifolds, showing their realizability as flat submanifolds.

Findings

Duality principle for submanifolds in pseudo-Euclidean spaces

Introduction of submanifolds with potential normals

Realization of Frobenius manifolds as flat submanifolds

Abstract

We prove a duality principle for a special class of submanifolds in pseudo-Euclidean spaces. This class of submanifolds with potential of normals is introduced in this paper. We prove also, for example, that an arbitrary Frobenius manifold can be realized as a certain flat submanifold of this very natural class.