On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons

Xu Cheng; Ernani Ribeiro; Detang Zhou

doi:10.1090/bproc/155

journal article Open Access Feb 27, 2023

On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons

Xu Cheng

Ernani Ribeiro Detang Zhou

Proceedings of the American Mathematical Society, Series B Vol. 10 No. 3 pp. 33-45 · American Mathematical Society (AMS)

View at Publisher Save 10.1090/bproc/155

Abstract

In this article, we investigate the geometry of

4
4

-dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a

4
4

-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.

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Details

Published: Feb 27, 2023
Vol/Issue: 10(3)
Pages: 33-45
License: View

Authors

Funding

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico Award: 403344/2021-2 and 305364/2019-7

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro Award: 403344/2021-2 and 305364/2019-7

Cite This Article

Xu Cheng, Ernani Ribeiro, Detang Zhou (2023). On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons. Proceedings of the American Mathematical Society, Series B, 10(3), 33-45. https://doi.org/10.1090/bproc/155

On Euler characteristic and Hitchin-Thorpe inequality for four-dimensional compact Ricci solitons

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