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...Riemannian geometry of di s revisited mariagordina abstract afurtherstudyofriemanniangeometrydi ispresented wedescribe hermitian and metrics on the complexication homogeneous space as well complexied symplectic form it is based ideas from where instead using k ahler structure symmetries to compute ricci curvature authors rely classical nite dimensional results nomizu et al spaces table contents introduction acknowledgment virasoro algebra a manifold references let be group orientation preserving dieomorphisms unit circle then quotient describes those dieomor phisms that x point this innite has been interest physicists e g we follow approach taken in describe an complex with metric theorem properties introduce covariant derivative which consistent use expression for found were used setting goal present article clarify certain parts particular stated question levi civita but details omitted paper explicitly dene proven part complete exposition computation tensor proof follows one date ap...