Kahler submanifolds and the Umehara algebra

TL;DR

This paper investigates the relationships between certain complex submanifolds and algebraic structures, demonstrating that indefinite Euclidean complex spaces are not relatives of indefinite non-flat complex space forms, and examining the relativity of compact Fubini-Study spaces.

Contribution

It provides new results on the non-relativity of indefinite Euclidean complex spaces with indefinite non-flat complex space forms and explores the conditions under which compact Fubini-Study spaces are relatives.

Findings

Indefinite Euclidean complex space is not a relative of indefinite non-flat complex space form.

Studied whether two compact Fubini-Study spaces are relatives.

Established criteria for relativity among these complex spaces.

Abstract

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not.