<p>In this paper, we classify 3-dimensional complete self-expanders in the Euclidean space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2024_2343_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb R^{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation> with constant squared norm <i>S</i> of the second fundamental form under the condition of constant <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2024_2343_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(f_{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>f</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation>.</p>

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Complete Self-expanders in the Euclidean Space \(\mathbb R^{4}\)

  • Zhi Li,
  • Yuan Mi

摘要

In this paper, we classify 3-dimensional complete self-expanders in the Euclidean space \(\mathbb R^{4}\) R 4 with constant squared norm S of the second fundamental form under the condition of constant \(f_{4}\) f 4 .