Sasaki-Einstein and paraSasaki-Einstein metrics from (κ,μ)-structures
We prove that every contact metric (κ, µ)-space admits a canonical η-Einstein Sasakian or η-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find the values of κ and µ for which such metrics are Sasaki-Einstein and paraSasakiEinste...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versión enviada para evaluación y publicación |
| Data de publicação: | 2013 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositório: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47076 |
| Acesso em linha: | http://hdl.handle.net/11441/47076 https://doi.org/10.1016/j.geomphys.2013.05.001 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Contact metric manifold Sasakian Paracontact ParaSasakian Nullity distribution (κ, µ)-spaces Einstein η-Einstein Legendre foliation Weyl structure Lorentzian Sasakian Tangent sphere bundle |
| Resumo: | We prove that every contact metric (κ, µ)-space admits a canonical η-Einstein Sasakian or η-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find the values of κ and µ for which such metrics are Sasaki-Einstein and paraSasakiEinstein. Conversely, we prove that, under some natural assumptions, a K-contact or K-paracontact manifold foliated by two mutually orthogonal, totally geodesic Legendre foliations admits a contact metric (κ, µ)-structure. Furthermore, we apply the above results to the geometry of tangent sphere bundles and we discuss some geometric properties of (κ, µ)-spaces related to the existence of EisteinWeyl and Lorentzian Sasaki-Einstein structures. |
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