English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we introduce a $\theta$-family of spacelike surfaces in theLorentz-Minkowski space R^4_1 based in two complex valued functions $a(w),\mu(w)$, which when they are holomorphic we will be dealing with a family ofspacelike minimal surfaces. The $\theta$-family is such that it connectsspacelike minimal surfaces in R^3_1 to spacelike minimal surfaces in R^3. Westudy the family through of the curvature and we prove that the familypreserves planar points and moreover, that the existence of planar pointscorresponds to the existence of solutions of equation |a_w(w)|^2 =0. We alsoshow that if a pair of surfaces are associated through of a $\theta$-familythen they can not be complete surfaces. As applications we focus to one type ofgraph surfaces in R^4_1 and we prove that if the imaginary part of $a(w)$ iszero at least in a point then the surface cannot assume local representationsof that type of graph. Several explicit examples are given.

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