Conformal Riemannian morphisms between Riemannian manifolds

In this article we introduce conformal Riemannian morphisms. The idea of conformal Riemannian morphism generalizes the notions of an isometric immersion, a Riemannian submersion, an isometry, a Riemannian map and a conformal Riemannian map. We show that every injective conformal Riemannian morphism is an injective conformal immersion, and that on a connected manifold, every surjective conformal Riemannian morphism is a surjective conformal submersion, and every bijective conformal Riemannian morphism is a conformal map

Assessing Tolerance to Heavy-Metal Stress in Arabidopsis thaliana Seedlings

The deposited book chapter is a post-print version and has been submitted to peer review.The deposited book chapter version contains attached the supplementary materials within the pdf.This publication hasn't any creative commons license associated.The deposited book chapter is part of the book series: "Environmental Responses in Plants: Methods and Protocols" (pp.197-208) published by Springer.Heavy-metal soil contamination is one of the major abiotic stress factors that, by negatively affecting plant growth and development, severely limit agricultural productivity worldwide. Plants have evolved various tolerance and detoxification strategies in order to cope with heavy-metal toxicity while ensuring adequate supply of essential micronutrients at the whole-plant as well as cellular levels. Genetic studies in the model plant Arabidopsis thaliana have been instrumental in elucidating such mechanisms. The root assay constitutes a very powerful and simple method to assess heavy-metal stress tolerance in Arabidopsis seedlings. It allows the simultaneous determination of all the standard growth parameters affected by heavy-metal stress (primary root elongation, lateral root development, shoot biomass, and chlorophyll content) in a single experiment. Additionally, this protocol emphasizes the tips and tricks that become particularly useful when quantifying subtle alterations in tolerance to a given heavy-metal stress, when simultaneously pursuing a large number of plant lines, or when testing sensitivity to a wide range of heavy metals for a single line.Fundação para a Ciência e a Tecnologia grants: (EXPL/AGR-PRO/1013/2013, SFRH/BPD/44640/2008); GREEN-it "Bioresources for Sustainability": (UID/Multi/04551/2013).info:eu-repo/semantics/publishedVersio

Cohomology and deformation of compatible Hom-Leibniz algebras

In this paper, we consider compatible Hom-Leibniz algebra where the Hom map twists the operations in the compatible system. We consider a suitably graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Hom-Leibniz algebras. Using this, we study cohomology, infinitesimal deformations, the Nijenhuis operator, and their relation for compatible Hom-Leibniz algebras. Finally we see the cohomology of compatible Hom-Leibniz algebra with coefficients in an arbitrary representation.Comment: arXiv admin note: substantial text overlap with arXiv:2306.0610

Cohomology and deformations of compatible Leibniz algebras

In this paper we study a cohomology theory of compatible Leibniz algebra. We construct a graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible Leibniz algebras. Using this, we study cohomology, infinitisimal deformations, Nijenhuis operator and their relation for compatible leibniz algebras. Finally using cohomology of compatible Leibniz algebra with coefficients in an arbitrary representation we study the abelian extensions of compatible Leibniz algebra.Comment: 20 page