Sectional curvature and Weitzenb\"ock formulae

We establish a new algebraic characterization of sectional curvature bounds $\sec\geq k$ and $\sec\leq k$ using only curvature terms in the Weitzenb\"ock formulae for symmetric $p$-tensors. By introducing a symmetric analogue of the Kulkarni-Nomizu product, we provide a simple formula for such curvature terms. We also give an application of the Bochner technique to closed $4$-manifolds with indefinite intersection form and $\sec>0$ or $\sec\geq0$, obtaining new insights into the Hopf Conjecture, without any symmetry assumptions.Comment: LaTeX2e, 25 pages, final version. To appear in Indiana Univ. Math.

Strongly positive curvature

We begin a systematic study of a curvature condition (strongly positive curvature) which lies strictly between positive curvature operator and positive sectional curvature, and stems from the work of Thorpe in the 1970s. We prove that this condition is preserved under Riemannian submersions and Cheeger deformations, and that most compact homogeneous spaces with positive sectional curvature satisfy it.Comment: LaTeX2e, 26 page

Controle biológico da podridão de raízes causada por Pythium spp. em cultivos hidropônicos.

bitstream/item/12263/1/documentos_77.pd

A comprehensive review of climate change and plant diseases in Brazil.

Analyzing the impacts of climate change on phytosanitary problems in Brazil is crucial due to the country’s special role in global food security as one of the largest producers of essential commodities. This review focuses on the effects of climate change on plant diseases and discusses its main challenges in light of Brazil’s diverse agricultural landscape. To assess the risk of diseases caused by fungi, bacteria, viruses, oomycetes, nematodes, and spiroplasms, we surveyed 304 pathosystems across 32 crops of economic importance from 2005 to 2022. Results show that diseases caused by fungi account for 79% of the pathosystems evaluated. Predicting the occurrence of diseases in a changing climate is a complex challenge, and the continuity of this work is strategic for Brazil’s agricultural defense. The future risk scenarios analyzed here aim to help guide disease mitigation for cropping systems. Despite substantial progress and ongoing efforts, further research will be needed to effectively prevent economic and environmental damage

Bibliografia brasileira de sementes: análise quantitativa.

bitstream/item/100432/1/Bibliog-sementes-brasileira.pd