%0 Journal Article
%T 半C-可约共形双扭曲积芬斯勒度量<br>Semi-C-Reducible Conformally Doubly Warped Product Finsler Metric
%A 加依达尔·里扎别克
%A 何勇
%A 杨蕊嘉
%A 陈静雅
%J Pure Mathematics
%P 330-337
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/PM.2025.154136
%X 设F<sub>1</sub>和F<sub>2</sub>分别是光滑流形M<sub>1</sub>和M<sub>2</sub>上的芬斯勒度量，共形双扭曲积芬斯勒度量是在乘积流形M=M<sub>1</sub>×M<sub>2</sub>上赋予的芬斯勒度量<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">
  <mi>F</mi>
  <mn>2</mn>
  <mo>=</mo>
  <mi>e</mi>
  <mn>2</mn>
  <mo> </mo>
  <mo stretchy=\"false\">(</mo>
  <mi>f</mi>
  <mn>2</mn>
  <mn>2</mn>
  <mi>F</mi>
  <mn>2</mn>
  <mn>1</mn>
  <mo>+</mo>
  <mi>f</mi>
  <mn>2</mn>
  <mn>1</mn>
  <mi>F</mi>
  <mn>2</mn>
  <mn>2</mn>
  <mo stretchy=\"false\">)</mo>
  <mo>,</mo>
  <mi>&#xD9;</mi>
</math>, 其中f<sub>1</sub>、f<sub>2</sub>和$\sigma$分别是M<sub>1</sub> 、M<sub>2</sub>和M上的正值光滑函数。本文证明了半C-可约共形双扭曲积芬斯勒度量是类C<sub>2</sub>芬斯勒度量。<br>Let F<sub>1</sub> and F<sub>2</sub>  be two Finsler metrics on smooth manifold M<sub>1</sub> and M<sub>2</sub>,respectively.The  conformally doubly warped product Finsler metric<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">
  <mi>F</mi>
  <mn>2</mn>
  <mo>=</mo>
  <mi>e</mi>
  <mn>2</mn>
  <mo> </mo>
  <mo stretchy=\"false\">(</mo>
  <mi>f</mi>
  <mn>2</mn>
  <mn>2</mn>
  <mi>F</mi>
  <mn>2</mn>
  <mn>1</mn>
  <mo>+</mo>
  <mi>f</mi>
  <mn>2</mn>
  <mn>1</mn>
  <mi>F</mi>
  <mn>2</mn>
  <mn>2</mn>
  <mo stretchy=\"false\">)</mo>
  <mo>,</mo>
  <mi>&#xD9;</mi>
</math>  is a Finsler metric endowed on the M=M<sub>1</sub>×M<sub>2</sub> ,where f<sub>1</sub>、f<sub>2</sub> and $\sigma$ are positive smooth functions onM<sub>1</sub> 、M<sub>2</sub> and M, respectively.It is proved that semi-C-reducible conformally doubly warped product Finsler metric is a C<sub>2</sub>.
%K 芬斯勒度量，共形双扭曲积，半C-可约芬斯勒度量，类C<sub>2</sub>芬斯勒度量<br>Finsler Meric
%K Conformally Doubly Warped Product
%K Semi-C-Reducible Finsler Metric
%K C<sub>2-</sub>Like Finsler Metric
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=113236