J. P. dos Santos

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20192025

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7 papers · 1 filter

math.DG2025

Rigidity of Translation Surfaces in the Three-Dimensional Sphere $S^{3}$

Tarcios Andrey Ferreira, João Paulo dos Santos

A translation surface in the three-dimensional sphere $S^{3}$ is a surface generated by the quaternionic product of two curves, called generating curves. In this paper, we p…

math.DG2024

Hypersurfaces of $S^{3} \times R$ and $H^{3} \times R$ with constant principal curvatures

Fernando Manfio, João Batista Marques dos Santos, João Paulo dos Santos +1

We classify the hypersurfaces of $Q^{3} \times R$ with three distinct constant principal curvatures, where $ε \in {1, - 1}$ and $Q^{3}$ denotes the u…

math.DG2021

Totally Umbilical Hypersurfaces of Product Spaces

Ronaldo F. de Lima, João Paulo dos Santos

Given a Riemannian manifold $M,$ and an open interval $I \subset R,$ we characterize nontrivial totally umbilical hypersurfaces of the product $M \times I$ -- as well as of w…

math.DG2020

Mean convex properly embedded $[φ, e_{3}]$ -minimal surfaces in $R^{3}$

Antonio Martínez, A. L. Martínez-Triviño, J. P. dos Santos

We establish curvature estimates and a convexity result for mean convex properly embedded $[φ, e_{3}]$ -minimal surfaces in $R^{3}$ , i.e., $φ$ -minimal surfaces when $φ$ …

math.DG2020

Hypersurfaces of Constant Higher Order Mean Curvature in $M \times R$

R. F. de Lima, F. Manfio, J. P. dos Santos

We consider hypersurfaces of products $M \times R$ with constant $r$ -th mean curvature $H_{r} \geq 0$ (to be called $H_{r}$ -hypersurfaces), where $M$ is an arbitrary Riemannian $n$ …

math.DG2020

Cyclic conformally flat hypersurfaces revisited

João Paulo dos Santos, Ruy Tojeiro

In this article we classify the conformally flat Euclidean hypersurfaces of dimension three with three distinct principal curvatures of $R^{4}$ , $\mathbb{S}^3\times \mathbb{…

math.DG2019

Einstein hypersurfaces of $S^{n} \times R$ and $H^{n} \times R$

Benedito Leandro, Romildo Pina, João Paulo dos Santos

In this paper, we classify the Einstein hypersurfaces of $S^{n} \times R$ and $H^{n} \times R$ . We use the characterization of the hypersurfaces of…

Rigidity of Translation Surfaces in the Three-Dimensional Sphere S3

Hypersurfaces of S3×R and H3×R with constant principal curvatures

Totally Umbilical Hypersurfaces of Product Spaces

Mean convex properly embedded [φ,e3​]-minimal surfaces in R3

Hypersurfaces of Constant Higher Order Mean Curvature in M×R

Cyclic conformally flat hypersurfaces revisited

Einstein hypersurfaces of Sn×R and Hn×R

Rigidity of Translation Surfaces in the Three-Dimensional Sphere $S^{3}$

Hypersurfaces of $S^{3} \times R$ and $H^{3} \times R$ with constant principal curvatures

Mean convex properly embedded $[φ, e_{3}]$ -minimal surfaces in $R^{3}$

Hypersurfaces of Constant Higher Order Mean Curvature in $M \times R$

Einstein hypersurfaces of $S^{n} \times R$ and $H^{n} \times R$