Deformations of 2k-Einstein structures

TL;DR

This paper investigates the deformation space of 2k-Einstein structures on compact space forms, demonstrating finiteness and rigidity results, especially for spherical cases.

Contribution

It establishes the finite dimensionality of infinitesimal deformations and proves the rigidity of spherical space forms within the moduli space.

Findings

Infinitesimal deformation space is finite dimensional for non-flat space forms.

Spherical space forms are rigid and isolated in the moduli space.

Results apply to compact non-flat 2k-Einstein structures.

Abstract

It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional at compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding moduli space.