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TitleTangent lie groups are Riemannian naturally reductive spaces
Author(s)Agricola, Ilka
Ferreira, Ana Cristina
KeywordsTangent Lie group
Riemannian naturally reductive homogeneous space
Characteristic connection
Almost Hermitian structure
Issue dateJun-2017
PublisherSpringer Verlag
JournalAdvances in Applied Clifford Algebras
Abstract(s)Given a compact Lie group G with Lie algebra gg, we consider its tangent Lie group TG≅G⋉AdgTG. In this short note, we prove that TG admits a left-invariant naturally reductive Riemannian metric g and a metric connection with skew torsion ∇∇ such that (TG,g,∇) is naturally reductive. An alternative spinorial description of the same connection on the direct product G×g generalizes in a rather subtle way to TS7, which is in many senses almost a tangent Lie group.
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AccessRestricted access (UMinho)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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