A Riemannian Einstein solvmanifold is called standard, if the orthogonal complement to the nilradical of its Lie algebra is abelian. No examples of nonstandard solvmanifolds are known. We show that the standardness of an Einstein metric solvable Lie algebra is completely detected by its nilradical and prove that many classes of nilpotent Lie algebras (Einstein nilradicals, algebras with less th...

Abstract A relevant property of equifocal submanifolds is that their parallel sets are still immersed submanifolds, which makes them a natural generalization the so-called isoparametric submanifolds. In this paper, we prove regular fibers an analytic map π : M m+k → B k whenever endowed with complete Finsler metric and there restriction submersion for certain on image. addition, when provide si...

Suppose M a compact manifold which admits an Einstein metric g which is Kähler with respect to some complex structure J . Is every other Einstein metric h on M also Kähler-Einstein? If the complex dimension of (M,J) is ≥ 3, the answer is generally no; for example, CP3 admits both the FubiniStudy metric, which is Kähler-Einstein, and a non-Kähler Einstein metric [2] obtained by appropriately squ...

Based on the previous research, in this paper we study the dual flatness of a special class of Finsler metrics called general (α, β)-metrics, which is defined by a Riemannian metric α and a 1-form β. By using a new kind of deformation technique, we construct many non-trivial explicit dually flat general (α, β)-metrics.