Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds |
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Authors: | Hiroshi Tamaru |
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Institution: | 1.Department of Mathematics,Hiroshima University,Higashi-Hiroshima,Japan |
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Abstract: | In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These
solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci curvatures
of our solvmanifolds coincide with the restrictions of the Ricci curvatures of the ambient symmetric spaces. Consequently,
all of our solvmanifolds are Einstein, which provide a large number of new examples of noncompact homogeneous Einstein manifolds.
We also show that our solvmanifolds are minimal, but not totally geodesic submanifolds of symmetric spaces. |
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Keywords: | |
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