Homogeneous Einstein Spaces with Negative Scalar

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 40724 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fannaei, Hammid Reza
Abstract:
All known examples of homogeneous Einstein spaces with negative scalar curvature (non compact) are isometric to standard Einstein solvmanifolds . we prove that any nilpotent Lie algebra having a codimension-one abelian ideal is the nilradical of a rank –one Einstein solvmanifold . In other words this nilpotent Lie algebra admits a rank-one solvable extension which can be endowed with an Einstein left invariant Riemannian metric . also a curve of pairwise non-isometric 8-dimensional rank-one Einstein solvmanifold is given .
Keywords:
Homogeneous Space ; Eigen Values ; Einstein Manifold ; Solvmanifold ; Nilradical

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