Related papers: On Einstein square metrics
We study the cylindrical symmetric Finsler metrics. We obtain the system of differential equations of such metrics which are projectively flat. We give a family of solutions of this system. Examples are included.
In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metrics with Douglas type must be Randers metrics or Berwald…
This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…
Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool…
A formalism (zeta-complex analysis), allowing one to construct global Einstein metrics by matching together local ones described in the papers Phys. Lett. B 513(2001)142-146; Diff. Geom. Appl. 16(2002)95-120, is developed. With this…
In a recent article the first three authors proved that in dimension $4m+1$ all homotopy spheres that bound parallelizable manifolds admit Einstein metrics of positive scalar curvature which, in fact, are Sasakian-Einstein. They also…
Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate…
We show that Hermitian-Einstein metrics can be locally constructed by a map from (anti-)self-dual two-forms on Euclidean ${\mathbb R}^4$ to symmetric two-tensors introduced in "Gravitational instantons from gauge theory," H. S. Yang and M.…
Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1…
In this paper we construct a new class of harmonic and asymptotically harmonic Finsler manifolds of $({\alpha},\beta)$-type. This class is defined by a Riemannian metric ${\alpha}$ and a special 1-form $\beta$.
We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
We show how to construct new Finsler metrics, in two and three dimensions, whose indicatrices are pedal curves or pedal surfaces of some other curves or surfaces. These Finsler metrics are generalizations of the famous slope metric, also…
Homogeneous geodesics of homogeneous Finsler metrics derived from two or more Riemannian geodesic orbit metrics are investigated. For a broad newly defined family of positively related Riemannian geodesic orbit metrics, geodesic lemma is…
The classification of Riemannian manifolds by the holonomy group of their Levi-Civita connection picks out many interesting classes of structures, several of which are solutions to the Einstein equations. The classification has two parts.…
The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified.…
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…
A construction of Kaehler-Einstein metrics using Galois coverings, studied by Arezzo-Ghigi-Pirola, is generalized to orbifolds. By applying it to certain orbifold covers of P^n which are trivial set theoretically, one obtains new Einstein…
In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…
We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…