Indefinite extrinsic symmetric spaces I

TL;DR

This paper establishes a correspondence between full extrinsic symmetric spaces in inner product spaces and algebraic structures called extrinsic symmetric triples, enabling a new algebraic description of these geometric objects.

Contribution

It introduces a novel one-to-one correspondence linking extrinsic symmetric spaces with algebraic triples, providing an algebraic framework for their classification.

Findings

Characterization of extrinsic symmetric spaces via algebraic triples

Description of arbitrary extrinsic symmetric spaces in pseudo-Euclidean spaces

Establishment of a bijective correspondence between geometric and algebraic structures

Abstract

We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of arbitrary extrinsic symmetric spaces in pseudo-Euclidean spaces by corresponding infinitesimal objects.