Bianchi-IX, Darboux-Halphen and Chazy-Ramanujan

Autor(es)

Chanda, Sumanto ^[1] ; Guha, Partha ^[1] ; Roychowdhury, Raju ^[2]

Afiliação do(s) autor(es)

^[1] SN Bose Natl Ctr Basic Sci, JD Block, Sect 3, Kolkata 700098 - India

^[2] Univ Sao Paulo, Inst Fis, C Postal 66318, BR-05314970 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS; v. 13, n. 4 APR 2016.
• Citações Web of Science: 3

Resumo

Bianchi-IX four metrics are SU(2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler top, while the curvaturewise self-dual case yields the Ricci flat classical Darboux-Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux-Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang-Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux-Halphen system and occurring in the study of Bianchi-IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability. (AU)

• Processo FAPESP: 13/17765-0 - Gravitação Emergente e Geometria Não-comutativa
• Beneficiário: Raju Roychowdhury
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado