July 4, 2024Open Access

Foliations transverse to a closed conformal vector field

ESEuripedes Carvalho da SilvaInstituto Federal de Educação, Ciência e Tecnologia do Ceará ÍGÍcaro GonçalvesUniversidade Federal do ABC JPJúlio PereiraInstituto Federal de Educação, Ciência e Tecnologia Baiano

Key Points

Totally geodesic leaves arise from foliations transverse to Montiel foliations, impacting their geometric properties.
A key finding relates minimal leaves and constant mean curvature foliations with unique characteristics.
Observational analysis of codimension one foliations with closed conformal vector fields reveals interesting geometric structures and constraints on leaves and ambient space geometry, leading to Montiel foliations. Characterization of totally geodesic foliations is achieved through their connections to previously defined Montiel foliations.

Abstract

In this article, we study the geometric properties of codimension one foliations on Riemannian manifolds equipped with vector fields that are closed and conformal. Apart from its singularities, these vector fields define codimension one foliations with nice geometric features, which we call Montiel Foliations. We investigate conditions for which a foliation transverse to this structure has totally geodesic leaves, as well as how the ambient space and the geometry of the leaves forces a given foliation into a Montiel Foliation. Our main results concern minimal leaves and constant mean curvature foliations, having compact or complete noncompact leaves. Finally, we characterize totally geodesic foliations by means of its relation to a prior Montiel Foliation.

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Cite This Study

Silva et al. (Thu,) studied this question.

synapsesocial.com/papers/68e616ccb6db6435875a99b7 https://doi.org/https://doi.org/10.48550/arxiv.2407.03989

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