New examples of non-symmetric Einstein solvmanifolds of negative Ricci curvature
نویسنده
چکیده
We obtain new examples of non-symmetric Einstein solvmanifolds by combining two techniques. In Tamaru (Parabolic subgroups of semisimple Lie groups and einstein solvmanifolds. Math Ann 351(1):51–66, 2011) constructs new attached solvmanifolds, which are submanifolds of the solvmanifolds correspond to noncompact symmetric spaces, endowed with a natural metric. Extending this construction, we apply it to associated solvmanifolds, described in (Ann Global Anal Geom 19(1):75–101, 2001), obtained by modifying the algebraic structure of the solvable Lie algebras corresponding to noncompact symmetric spaces. Our new examples are Einstein solvmanifolds with nilradicals of high nilpotency, which are geometrically distinct from noncompact symmetric spaces and their submanifolds.
منابع مشابه
Parabolic Subgroups of Semisimple Lie Groups and Einstein Solvmanifolds
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...
متن کاملA Deformation of Quaternionic Hyperbolic Space
We construct a continuous family of new homogeneous Einstein spaces with negative Ricci curvature, obtained by deforming from the quaternionic hyperbolic space of real dimension 12. We give an explicit description of this family, which is made up of Einstein solvmanifolds which share the same algebraic structure (eigenvalue type) as the rank one symmetric space HH. This deformation includes a c...
متن کاملTotally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures
In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملA Characterization of Noncompact Koiso-type Solitons
We construct complete gradient Kähler–Ricci solitons of various types on the total spaces of certain holomorphic line bundles over compact Kähler–Einstein manifolds with positive scalar curvature. Those are noncompact analogues of the compact examples found by Koiso [On rotationally symmetric Hamilton’s equations for Kähler–Einstein metrics, in Recent Topics in Differential and Analytic Geometr...
متن کامل