arXiv subjects

Llohann Dallagnol Sperança

Publications and source records attributed to Llohann Dallagnol Sperança.

2 recordsLinked to original sources

arXiv2023

A direct approach to prescribing scalar curvature on bundles

This note intends to demonstrate how to discuss scalar curvature functions' admissibility on bundles by directly applying some of the Kazdan--Warner results. Proofs of the concept include determining which functions are realizable as scalar curvature functions on the total space of several bundles over exotic manifolds. In addition, we employ traditional variational methods to provide reasonable conditions to smooth functions on the total spaces of some fiber bundles to be realized as scalar curvature functions for some Riemannian submersions metrics. We apply these last results to bundles over Calabi--Yau manifolds.

math.DG↗

arXiv2020

Positive Ricci curvature on fiber bundles with compact structure group

The aim of this paper is to present a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it also generalizes and puts in a unified framework the results in Nash \cite{nash} and Poor \cite{poor}. With the intention of disseminating this result, we apply it to build new examples of manifolds with positive Ricci curvature, including bundles whose base consists of gradient shrinking Ricci solitons.

math.DG↗