Counterexamples to Goldberg Conjecture on neutral 4-manifolds and higher dimensional indefinite metric spaces with attention to the reversed orientation

Yasuo Matsushita - Osaka

Luns 13 de marzo de 2017 ás 10 horas na aula 4.

Resumo:

My talk will begin with a survey on Goldberg Conjecture (1969) which states that an almost complex structure on a compact almost-Kähler Einstein manifold in integrable. There are many works on Goldberg Conjecture on Riemannian geometry, which are concerned mainly with an almost complex structure of normal orientation

On the other hand, certain counterexamples of indefinite metric spaces are already reported, which exhibit nonintegrability of both an almost complex structure and also an opposite almost complex structure. From these analysis, I will discuss on the indefinite metric spaces endowed with two kinds of almost complex structures, and consider the crucial difference between normal and reversed orientations.