Shells of monotone curves

Mikeš, Josef; Strambach, Karl

doi:10.1007/s10587-015-0202-5

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Introduction3

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Elementary Geometry and Geodesics1

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Cited by 8 publications

(6 citation statements)

References 13 publications

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“…In addition, Saglam, Soytürk, and Sabuncuoǧlu gave a connection of minimal translation surfaces with geodesic planes, and Hasanis and Lóez gave the classification of minimal translation surfaces in Euclidean space. The present paper is close to the research of Belova, Mikeš, and Strambach [22][23][24][25], where similar methods for investigations of geodesics and almost geodesics were used.…”

Section: Theoremmentioning

confidence: 54%

A Note on Minimal Translation Graphs in Euclidean Space

Yang

Zhang

2019

Mathematics

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In this note, we give a characterization of a class of minimal translation graphs generated by planar curves. Precisely, we prove that a hypersurface that can be written as the sum of n planar curves is either a hyperplane or a cylinder on the generalized Scherk surface. This result can be considered as a generalization of the results on minimal translation hypersurfaces due to Dillen–Verstraelen–Zafindratafa in 1991 and minimal translation surfaces due to Liu–Yu in 2013.

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Section: Theoremmentioning

confidence: 54%

A Note on Minimal Translation Graphs in Euclidean Space

Yang

Zhang

2019

Mathematics

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“…This paper is a result following on from D. Betten researchs [4] and our papers [1,[8][9][10]. The geodesics and almost geodesics play an important role in differential geometry.…”

Section: Introductionmentioning

confidence: 80%

About almost geodesic curves

Belova

Mikeš

Strambach

2019

Filomat

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“…In [21] J. Mikeš and K. Strambach have determined the form of curves C in R n corresponding to strictly monotone functions as well as the components of affine connections ∇ for which any image of C under a compact-free group of affinities containing the translation group is a geodesic with respect to ∇.…”

Section: Elementary Geometry and Geodesicsmentioning

confidence: 99%