Related papers: A note on Codazzi tensors

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…

We study some properties of a $3$-dimensional manifold with a diagonal Riemannian metric as an almost $\eta$-Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if $\eta$ is…

The Ponzano-Regge model of three-dimensional quantum gravity is well-defined when the observables satisfy a certain condition involving the twisted cohomology. In this case, the partition function is defined in terms of the Reidemeister…

By excluding some sets, which don't include any eigenvalue of a tensor, from some existing eigenvalue inclusion sets, two new sets are given to locate all eigenvalues of a tensor. And it is shown that these two sets are contained in the…

We introduce the notion of a special monopole class on a four-manifold. This is used to prove restrictions on the smooth structures of Einstein manifolds. As an application we prove that there are Einstein four-manifolds which are simply…

We obtain new topological restrictions for complete Riemannian manifolds with nonnegative Ricci curvature and RCD(0,n) spaces. Our main results are a Betti number rigidity theorem which answers a question open since work of M.-T. Anderson…

Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor are studied. Their existence, classification and explicit local expression are considered. Related issues and open questions are briefly commented.

This paper addresses two fundamental problems posed by Qi regarding the sufficiency of eigenvalues for the classification of symmetric tensors in the two-dimensional setting. For $2\times2\times2$ and $2\times2\times2\times2$ complex…

It is well known that an $m$-dimensional Riemannian manifold can be locally isometrically embedded into the $m+1$-dimensional Euclidean space if and only if there exists a symmetric 2-tensor field satisfying the Gauss and Codazzi equations.…

We study $3$-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz for constructing solitons in terms of data on…

In this paper we discuss Perelman's Lambda-functional, Perelman's Ricci shrinker entropy as well as the Ricci expander entropy on a class of manifolds with isolated conical singularities. On such manifolds, a singular Ricci de Turck flow…

Utilizing the covariant formulation of Penrose's plane wave limit by Blau et~al., we construct for any semi-Riemannian metric $g$ a family of "plane wave limits." These limits are taken along any geodesic of $g$, yield simpler metrics of…

Let $(M,g,J,\omega)$ be an almost Hermitian manifold. Given an automorphism $\psi\in \mathrm{Aut}(TM)$, the existing structure can be twisted to obtain a new almost Hermitian manifold $(M,g^\psi,J^\psi,\omega^\psi)$. In the current paper,…

We prove the Bloch conjecture : $ c_2(E) \in H^4_\cald (X,\bbz(2))$ is torsion for holomorphic rank two vector bundles $E$ with an integrable connection over a complex projective variety $X$. We prove also the rationality of the…

We study the algebraic features of covariant tensors of valence four containing two blocks of skew indices. After a rather general treatment, we specialize ourselves to four-dimensional spacetimes and discuss several complementary aspects…

We prove structure results for homogeneous spaces that support a non-constant solution to two general classes of equations involving the Hessian of a function and an invariant 2-tensor. We also consider trace-free versions of these systems.…

The Minkowski tensors are valuations on the space of convex bodies in ${\mathbb R}^n$ with values in a space of symmetric tensors, having additional covariance and continuity properties. They are extensions of the intrinsic volumes, and as…

We study 8-dimensional Riemannian manifolds that admit a PSU(3)-structure. We classify these structures by their intrinsic torsion and characterize the corresponding classes via differential equations. Moreover, we consider a connection…

In this paper, we study a three-dimensional Ricci-degenerate Riemannian manifold $(M^3,g)$ that admits a smooth nonzero solution $f$ to the equation \begin{align} \label{a1a} \nabla df=\psi Rc+\phi g, \end{align} where $\psi,\phi$ are given…

In the literature we see that after introducing a geometric structure by imposing some restrictions on Riemann-Christoffel curvature tensor, the same type structure given by imposing same restriction on other curvature tensors being…