Scholarlink

<p>We classify 7-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{G}_2\)</EquationSource> </InlineEquation>, up to naturally reductive homogeneous spaces and nearly parallel <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\textrm{G}_2\)</EquationSource> </InlineEquation>-structures. This extends and completes the classification initiated by Th. Friedrich in the cocalibrated case. Incidentally, we also obtain the list of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\textrm{SU}(3)\)</EquationSource> </InlineEquation> geometries with parallel skew-symmetric torsion, up to naturally reductive homogeneous spaces and nearly Kähler manifolds.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

\(\textrm{G}_2\)-structures with parallel skew-symmetric torsion

  • 期刊论文

  • 发表日期：

    2026年4月6日

查看全文
  • Andrei Moroianu,
  • Uwe Semmelmann

摘要

We classify 7-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in \(\textrm{G}_2\) , up to naturally reductive homogeneous spaces and nearly parallel \(\textrm{G}_2\) -structures. This extends and completes the classification initiated by Th. Friedrich in the cocalibrated case. Incidentally, we also obtain the list of \(\textrm{SU}(3)\) geometries with parallel skew-symmetric torsion, up to naturally reductive homogeneous spaces and nearly Kähler manifolds.