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Your search keyword '"Corro, Armando M. V."' showing total 15 results
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15 results on '"Corro, Armando M. V."'

1. New Flat surfaces in $S^3$

Author

Corro, Armando M. V. and Ferro, Marcelo Lopes

Subjects
Mathematics - Geometric Topology
Abstract

n this paper, we consider a method of constructing flat surfaces based on Ribaucour transformations in the sphere 3-space. By applying the theory to the flat torus, we obtain a families of complete flat surfaces in $S^3$ which are determined by several parameters. we provide explicit examples.

Published
2021

2. $\epsilon$-isothermic surfaces in pseudo-Euclidean 3-space

Author

Corro, Armando M. V., Riveros, Carlos M. C., and Ferro, Marcelo L.

Subjects
Mathematics - Geometric Topology
Abstract

In this paper we describe the $\epsilon$-isothermic surfaces in the pseudo-Euclidean 3-space and we obtain the pseudo-Calapso equation. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal curvatures and provide explicit coordinates for such surfaces. As application of the theory, we give explicit solutions to the pseudo-Calapso equation.

Published
2020

3. New Isothermic surfaces

Author

Corro, Armando M. V. and Ferro, Marcelo Lopes

Subjects
Mathematics - Geometric Topology, Mathematics - Differential Geometry
Abstract

In this paper, we consider a method of constructing isothermic surfaces based on Ribaucour transformations. By applying the theory to the cylinder, we obtain a three-parameter family of complete isothermic surfaces that contains n-bubble surfaces inside and outside of the cylinder. In addition, we also obtain one-parameter family of complete isothermic surface with planar ends. Such family of isothermic surfaces do not have constant mean curvature. As aplication we obtain explicit solutions of the Calapso equation.

Published
2020

4. A CLASS OF SOLUTIONS OF THE n-DIMENSIONAL GENERALIZED HELMHOLTZ EQUATION WHICH DESCRIBES GENERALIZED WEINGARTEN HYPERSURFACES.

Author

Corro, Armando M. V., Riveros, Carlos M. C., and Carretero, José L. T.

Subjects
HELMHOLTZ equation, HYPERSURFACES, BIHARMONIC functions, HOLOMORPHIC functions, BIHARMONIC equations
Abstract

In this paper, we introduce the n-dimensional generalized Helmholtz equation and present explicit solutions to this equation in terms of biharmonic functions, in particular, we get solutions that depend on holomorphic functions. Also, we present explicit radial solutions for this equation and we provide explicit solutions to the n-dimensional Helmholtz equation. In addition, as an application we introduced two classes of generalized Weingarten hypersurfaces, namely, the RSHGW-hypersurfaces and the RSGW-hypersurfaces, associated with solutions of the n-dimensional generalized Helmholtz equation and classify the RSHGW-hypersurfaces of rotation. For n = 2, we obtain a Weierstrass type representation for these surfaces which depend of three holomorphic functions and we classify the RSHGW-surfaces and the RSGW-surfaces of rotation. [ABSTRACT FROM AUTHOR]

Published
2024
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7. Ribaucour surfaces of harmonic type.

Author

Corro, Armando M. V., Riveros, Carlos M. C., and Fernandes, Karoline V.

Subjects
*ROTATIONAL motion, *CURVATURE
Abstract

We introduce the class of Ribaucour surfaces of harmonic type (in short HR-surfaces) that generalizes the Ribaucour surfaces related to a problem posed by Élie Cartan. We obtain a Weierstrass-type representation for these surfaces which depends on three holomorphic functions. As application, we classify the HR-surfaces of rotation, present examples of complete HR-surfaces of rotation with at most two isolated singularities and an example of a complete HR-surface of rotation with one catenoid type end and one planar end. Also, we present a 5-parameter family of cyclic HR-surfaces foliated by circles in non-parallel planes. Moreover, we classify the isothermic HR-surfaces with planar lines of curvature. [ABSTRACT FROM AUTHOR]

Published
2022
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9. Surfaces with Constant Chebyshev Angle II

Author

RIVEROS, Carlos M. C. and CORRO, Armando M. V.

Subjects
Physics::Computational Physics, General Mathematics, 30D30, 53A10, 35C99, Mathematics::Numerical Analysis
Abstract

In this paper we classify a class of surfaces with negative Gaussian curvature parametrized by a generalized Chebyshev net with constant Chebyshev angle in the Euclidean 3-space. As an application we obtain for each constant Chebyshev angle a seven-parameter family of complete surfaces.

Published
2013

15. A CHARACTERIZATION OF THE CATENOID AND HELICOID.

Author

HIVEROS, CARLOS M. C. and CORRO, ARMANDO M. V.

Subjects
*MINIMAL surfaces, *ASYMPTOTES, *GEODESICS, *CURVATURE, *GEOMETRIC surfaces, *MATHEMATICAL analysis
Abstract

In this paper we show that a connected non-planar minimal surface whose asymptotic lines have the same geodesic curvature up to sign is a catenoid. As an application of this result we show that a connected non-planar minimal surface whose lines of curvature have the same geodesic curvature up to sign is a helicoid. Moreover, we show that the coordinates curves of the associate minimal surfaces to catenoid have the same geodesic curvature up to sign. [ABSTRACT FROM AUTHOR]

Published
2013
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