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Submanifolds of higher rank with curvature normals of constant length
Santiago Castañeda-Montoya, Guillermo Lobos, Carlos Olmos
We study the local geometry of Euclidean submanifolds of rank at least two whose curvature normals with respect to the flat part of the normal bundle have constant length, equivale…
A Simons' type formula for spacelike submanifolds in semi-Riemannian warped product
Guillermo A. Lobos, Mynor Melara, Maria R. B. Santos
We determine a Simons' type formula for spacelike submanifolds within a broad class of semiRiemannian warped products. This formula extends the Simons' type formulas initially intr…
On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms
Nikos Georgiou, Guillermo Antonio Lobos Villagra
We prove that a deformation of a hypersurface in a -dimensional real space form induce a Hamiltonian variation of the normal congruence in the spac…
Explicit minimal Scherk saddle towers of arbitrary even genera in
A. J. Yucra Hancco, G. A. Lobos, V. Ramos Batista
Starting from works by Scherk (1835) and by Enneper-Weierstraß\ (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see \cite{Karcher1,Karcher}). In t…
Minimal surfaces with only horizontal symmetries
M. F. da Silva, G. A. Lobos, V. Ramos Batista
We find the first examples of triply periodic minimal surfaces of which the intrinsic symmetries are all of horizontal type.