Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A CHARACTERIZATION OF MAXIMAL SURFACES IN TERMS OF THE GEODESIC CURVATURES

  • Eunjoo Lee (Department of Mathematics Soongsil University)
  • Received : 2024.04.03
  • Accepted : 2024.05.08
  • Published : 2024.05.31
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Abstract

Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃3 in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.

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References

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