Related papers: On Sasaki-Einstein manifolds in dimension five

In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the…

Recently an infinite family of explicit Sasaki-Einstein metrics Y^{p,q} on S^2 x S^3 has been discovered, where p and q are two coprime positive integers, with q<p. These give rise to a corresponding family of Calabi-Yau cones, which…

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…

We study existence of invariant Einstein metrics on complex Stiefel manifolds $G/K = \SU(\ell+m+n)/\SU(n) $ and the special unitary groups $G = \SU(\ell+m+n)$. We decompose the Lie algebra $\frak g$ of $G$ and the tangent space $\frak p$ of…

We give a complete list of non-isometric bidimensional rotation invariant K\"ahler-Einstein submanifolds of a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves in the aforementioned case a…

We define K-stability of a polarized Sasakian manifold relative to a maximal torus of automorphisms. The existence of a Sasaki-extremal metric in the polarization is shown to imply that the polarization is K-semistable. Computing this…

It is an important problem in differential geometry to find non-naturally reductive homogeneous Einstein metrics on homogeneous manifolds. In this paper, we consider this problem for some coset spaces of compact simple Lie groups. A new…

This is an expository article. Among other topics, we discuss the existence of Kahler-Ricci soliton metrics on toric Fano manifolds, and Kahler-Einstein metrics on deformations of the Mukai-Umemura 3-fold

The aim of this paper is to construct infinitely many families of Einstein metrics on the connected sums of arbitrary number of copies of $S^2\times S^3$. We realize these 5-manifolds as total spaces of Seifert bundles over Del Pezzo…

We investigate holographic spectral functions for general Sasaki-Einstein 5-manifolds dual to four-dimensional superconformal field theories, including supersymmetric indices, supersymmetric zeta functions, and supersymmetric determinants.…

Several Einstein-Sasaki 7-metrics appearing in the physical literature are fibered over four dimensional Kahler-Einstein metrics. Instead we consider here the natural Kahler-Einstein metrics defined over the twistor space Z of any…

During an operation of surgery on a Riemannian manifold and along a given embedded submanifold, one needs to replace the (old) metric induced by the exponential map on a tubular neighborhood of the submanifold by the Sasakian metric. So a…

We classify compact simply-connected 5-dimensional manifolds which admit a metric of nonnegative curvature with a connected non-abelian group acting by isometries. We show that they are diffeomorphic to either S^5, S^3 x S^2, the nontrivial…

This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible homogeneous…

In the first part, we define and investigate new classes of almost 3-contact metric manifolds, with two guiding ideas in mind: first, what geometric objects are best suited for capturing the key properties of almost 3-contact metric…

We study compact Sasakian manifolds whose Tondeur connection has holonomy group either trivial or contained in Sp(n). We show that the first condition forces the manifold to be a compact quotient of the Heisenberg Lie group, while in the…

A gap in the proof of the main result in reference [1] in our original submission propagated into the constructions presented in the first version of our manuscript. In this version we give an alternative proof for the existence of…

Catino, Mastrolia, Monticelli, and Rigoli have launched an ambitious program to study known geometric solitons from a unified perspective, which they term Einstein-type manifolds. This framework allows one to treat Ricci solitons, Yamabe…

The aim of this paper is to construct left-invariant Einstein pseudo-Riemannian Sasaki metrics on solvable Lie groups. We consider the class of $\mathfrak z$-standard Sasaki solvable Lie algebras of dimension $2n+3$, which are in one-to-one…

We consider 5-manifolds with a contact form arising from a hypo structure, which we call \emph{hypo-contact}. We provide conditions which imply that there exists such a structure on an oriented hypersurface of a 6-manifold with a half-flat…