<p>We obtain the rigidity for local holomorphic isometric maps from <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2024_3080_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {B}^{n}, n \ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">B</mi> </mrow> <mi>n</mi> </msup> <mo>,</mo> <mi>n</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> into <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2024_3080_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="251" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {B}^{N_1} \times \cdots \times \mathbb {B}^{N_{m}}\times \mathbb {B}^{L_1} \times \cdots \times \mathbb {B}^{L_v}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">B</mi> </mrow> <msub> <mi>N</mi> <mn>1</mn> </msub> </msup> <mo>×</mo> <mo>⋯</mo> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">B</mi> </mrow> <msub> <mi>N</mi> <mi>m</mi> </msub> </msup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">B</mi> </mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> </msup> <mo>×</mo> <mo>⋯</mo> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">B</mi> </mrow> <msub> <mi>L</mi> <mi>v</mi> </msub> </msup> </mrow> </math></EquationSource> </InlineEquation> with respect to the normalized Bergman metrics up to conformal constants, which are allowed to be negative.</p>

Local holomorphic isometric maps from the complex unit ball into a product of complex unit balls: negative conformal constants

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发表日期：

2025年1月3日

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Xiaoliang Cheng,
Yihong Hao,
Yuan Yuan,
Xu Zhang

摘要

We obtain the rigidity for local holomorphic isometric maps from $\mathbb {B}^{n}, n \ge 2$ $B^{n}, n \geq 2$ into $\mathbb {B}^{N_1} \times \cdots \times \mathbb {B}^{N_{m}}\times \mathbb {B}^{L_1} \times \cdots \times \mathbb {B}^{L_v}$ $B^{N_{1}} \times \dots \times B^{N_{m}} \times B^{L_{1}} \times \dots \times B^{L_{v}}$ with respect to the normalized Bergman metrics up to conformal constants, which are allowed to be negative.