Einstein solvmanifolds and the pre-Einstein derivation
نویسندگان
چکیده
منابع مشابه
Einstein Solvmanifolds and the Pre-einstein Derivation
An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable ...
متن کاملHigher rank Einstein solvmanifolds
In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.
متن کاملsolvmanifolds with a simple Einstein derivation
The structure of a solvable Lie groups admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known ...
متن کاملEinstein solvmanifolds and nilsolitons
The purpose of the present expository paper is to give an account of the recent progress and present status of the classification of solvable Lie groups admitting an Einstein left invariant Riemannian metric, the only known examples so far of noncompact Einstein homogeneous manifolds. The problem turns to be equivalent to the classification of Ricci soliton left invariant metrics on nilpotent L...
متن کاملEinstein Solvmanifolds Are Standard
We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber [H] has showed that under certain simple algebraic condition (such a solvmanifold is called standard), Einstein solvmanifolds have many remarkable structural and uniqueness properties. In this p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2011
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2011-05045-2