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<p>We study heat kernel rigidity for the Lie group <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\text {SU}}\left( 2 \right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SU</mtext> <mfenced close=")" open="("> <mn>2</mn> </mfenced> </mrow> </math></EquationSource> </InlineEquation> equipped with a sub-Riemannian structure. We prove that a metric measure space equipped with a heat kernel of a special form is bundle-isometric to the Hopf fibration <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\text {U}}\left( 1 \right) \rightarrow {\text {SU}}\left( 2 \right) \rightarrow \mathbb{C}\mathbb{P}^1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>U</mtext> <mfenced close=")" open="("> <mn>1</mn> </mfenced> <mo stretchy="false">→</mo> <mtext>SU</mtext> <mfenced close=")" open="("> <mn>2</mn> </mfenced> <mo stretchy="false">→</mo> <mi mathvariant="double-struck">C</mi> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mn>1</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, which coincides with the sub-Riemannian sphere <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\text {SU}}\left( 2 \right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SU</mtext> <mfenced close=")" open="("> <mn>2</mn> </mfenced> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Rigidity of the Subelliptic Heat Kernel on \({\text {SU}}\left( 2 \right) \)

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Maria Gordina,
  • Jing Wang

摘要

We study heat kernel rigidity for the Lie group \({\text {SU}}\left( 2 \right) \) SU 2 equipped with a sub-Riemannian structure. We prove that a metric measure space equipped with a heat kernel of a special form is bundle-isometric to the Hopf fibration \({\text {U}}\left( 1 \right) \rightarrow {\text {SU}}\left( 2 \right) \rightarrow \mathbb{C}\mathbb{P}^1\) U 1 → SU 2 → C P 1 , which coincides with the sub-Riemannian sphere \({\text {SU}}\left( 2 \right) \) SU 2 .