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<p>We study the setting of 2-step nilpotent Lie groups in the particular case that its type (<i>p</i>,&#xa0;<i>q</i>) is not exceptional. We demonstrate that, generically, the orbits of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^{&gt;0}\times \operatorname {Aut}_0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mo>&gt;</mo> <mn>0</mn> </mrow> </msup> <mo>×</mo> <msub> <mo>Aut</mo> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> in <i>GL</i>(<i>n</i>)/<i>O</i>(<i>n</i>) are congruent even when a Ricci soliton metric does exists. In doing so, we provide a counterexample to the local version of a conjecture of Taketomi–Tamaru.</p>

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Concerning a conjecture of Taketomi–Tamaru

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Michael Jablonski

摘要

We study the setting of 2-step nilpotent Lie groups in the particular case that its type (p, q) is not exceptional. We demonstrate that, generically, the orbits of \(\mathbb {R}^{>0}\times \operatorname {Aut}_0\) R > 0 × Aut 0 in GL(n)/O(n) are congruent even when a Ricci soliton metric does exists. In doing so, we provide a counterexample to the local version of a conjecture of Taketomi–Tamaru.