On holomorphic Riemannian geometry and submanifolds of Wick-related spaces

TL;DR

This paper explores how holomorphic Riemannian geometry can connect submanifolds across different pseudo-Riemannian spaces, providing a theoretical framework for relating their geometric properties.

Contribution

It introduces a method using holomorphic Riemannian geometry to relate submanifolds in various pseudo-Riemannian spaces, extending existing background theory.

Findings

Establishes a framework for relating submanifolds across spaces

Extends background theory on holomorphic Riemannian manifolds

Provides tools for analyzing geometric properties in different spaces

Abstract

In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first rephrase and extend some background theory on holomorphic Riemannian manifolds, which is essential for the later application of the presented method.