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- W1490265136 abstract "We study surfaces defined as graph of the function<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>in the product space<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:msup><mml:mrow><mml:mi>ℍ</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle=italic>2</mml:mn></mml:mrow></mml:msup><mml:mo>×</mml:mo><mml:mi>ℝ</mml:mi></mml:math>. In particular, we completely classify flat or minimal surfaces given by<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi>f</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>u</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>+</mml:mo><mml:mi>v</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>u</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>v</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>are smooth functions." @default.
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- W1490265136 date "2014-01-01" @default.
- W1490265136 modified "2023-09-24" @default.
- W1490265136 title "Some Surfaces with Zero Curvature inℍ2×ℝ" @default.
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- W1490265136 doi "https://doi.org/10.1155/2014/154294" @default.
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