Related papers: Three-dimensional almost Kenmotsu manifolds satisf…

We provide classification results for and examples of half conformally flat generalized quasi Einstein manifolds of signature $(2,2)$. This analysis leads to a natural equation in affine geometry called the affine quasi-Einstein equation…

Given a closed Riemannian manifold $(N^{n+1},g)$, $n+1 \geq 3$ we prove the compactness of the space of singular, minimal hypersurfaces in $N$ whose volumes are uniformly bounded from above and the $p$-th Jacobi eigenvalue $\lambda_p$'s are…

The purpose of the article is to characterize \textbf{gradient $(m,\rho)$-quasi Einstein solitons} within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper.

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of…

We study compact almost complex manifolds admitting a Hermitian metric satisfying an integral condition involving $\overline \partial$-harmonic $(0,1)$-forms. We prove that this integral condition is automatically satisfied, if the…

We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions…

In this paper the notion of Ricci $\rho$-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3- dimensional almost Kenmotsu Einstein manifold $M$…

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…

We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and sufficient condition on the Weyl tensor for…

In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-\'Emery condition $BE (K, N)$. The sufficient condition is satisfied for the glued space of any two (not necessary same…

We study the properties of $\text{CAT}(\kappa)$ surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the $\text{CAT}(\kappa)$ condition locally. The main facts about…

In this paper we prove weak L^{1,p} (and thus C^{\alpha}) compactness for the class of uniformly mean-convex Riemannian n-manifolds with boundary satisfying bounds on curvature quantities, diameter, and (n-1)-volume of the boundary. We…

In this paper, we study two notions of rigidity, one of conformal submersions and the other of quasi Einstein manifolds, with an attempt to relate the two notions. Note that a smooth submersion between Riemannian manifolds is called…

Let $(X,g)$ be a compact Riemannian manifold with quasi-positive Riemannian scalar curvature. If there exists a complex structure $J$ compatible with $g$, then the canonical bundle $K_X$ is not pseudo-effective and the Kodaira dimension…

We classify flat strict nearly K\"ahler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-K\"ahler factor of maximal dimension and a strict flat nearly K\"ahler manifold of split…

We give a local classification of ({\kappa},{\mu},\u{psion}=const.)-contact metric manifold (M,{\phi},{\xi},{\eta},g) with {\kappa}<1 which satisfies the condition" the Boeckx invariant function I_{M}=((1-({\mu}/2))/(\surd(1-{\kappa}))) is…

We construct discrete versions of $\kappa$-Minkowski space related to a certain compactness of the time coordinate. We show that these models fit into the framework of noncommutative geometry in the sense of spectral triples. The dynamical…

We construct Kahler-Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2 or if the…

We deal with rigidity results for compact gradient Einstein-type manifolds with nonempty boundaries. As a result, we obtain new characterizations for hemispheres and geodesic balls in simply connected space forms. In dimensions three and…

It is shown that the first order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex…