arXiv subjects

R. S. Santos

Publications and source records attributed to R. S. Santos.

3 recordsLinked to original sources

arXiv2023

Spacelike minimal surfaces in R^4_1 through of a $θ$-Family

In this paper we introduce a $θ$-family of spacelike surfaces in the Lorentz-Minkowski space R^4_1 based in two complex valued functions $a(w), μ(w)$, which when they are holomorphic we will be dealing with a family of spacelike minimal surfaces. The $θ$-family is such that it connects spacelike minimal surfaces in R^3_1 to spacelike minimal surfaces in R^3. We study the family through of the curvature and we prove that the family preserves planar points and moreover, that the existence of planar points corresponds to the existence of solutions of equation |a_w(w)|^2 =0. We also show that if a pair of surfaces are associated through of a $θ$-family then they can not be complete surfaces. As applications we focus to one type of graph surfaces in R^4_1 and we prove that if the imaginary part of $a(w)$ is zero at least in a point then the surface cannot assume local representations of that type of graph. Several explicit examples are given.

math.DG↗

arXiv2021

Minimal spacelike surfaces and the graphic equations in R^4_1

In this paper we study an extension of the Bernstein Theorem for minimal spacelike surfaces of the four dimensional Minkowski vector space form and we obtain the class of those surfaces which are also graphics and have non-zero Gauss curvature. That is the class of entire solutions of a system of two elliptic non-linear equations that is an extension of the equation of minimal graphic of $\mathbb R^3$. Therefore, we prove that the so-called Bernstein property does not hold in general for the case of graphic spacelike surfaces in $\mathbb R^4_1$. In addition, we also obtain explicitly the conjugated minimal spacelike surface, and identify the necessary conditions to extend continuously a local solution of the generalized Cauchy-Riemann equations.

math.DG↗

arXiv2010

Why do dolphins form mixed-species associations in the Azores ?

Mixed-species associations are temporary associations between individuals of different species that are often observed in birds, primates and cetaceans. They have been interpreted as a strategy to reduce predation risk, enhance foraging success and/or provide a social advantage. In the archipelago of the Azores, four species of dolphins are commonly involved in mixed-species associations: the common dolphin, Delphinus delphis, the bottlenose dolphin, Tursiops truncatus, the striped dolphin, Stenella coeruleoalba, and the spotted dolphin, Stenella frontalis. In order to understand the reasons why dolphins associate, we analysed field data collected since 1999 by research scientists and trained observers placed onboard fishing vessels. In total, 113 mixed-species groups were observed out of 5720 sightings. The temporal distribution, habitat (water depth, distance to the coast), behaviour (i.e. feeding, travelling, socializing), size and composition of mixed-species groups were compared with those of single-species groups. Results did not support the predation avoidance hypothesis and gave little support to the social advantage hypothesis. The foraging advantage hypothesis was the most convincing. However, the benefits of mixed-species associations appeared to depend on the species. Associations were likely to be opportunistic in the larger bottlenose dolphin, while there seemed to be some evolutionary constraints favouring associations in the rarer striped dolphin. Comparison with previous studies suggests that the formation of mixed-species groups depends on several environmental factors, and therefore may constitute an adaptive response.

q-bio.PE↗