Related papers: Topological and Geometric Obstructions on Einstein…

We use a Hamiltonian version of the semiclassical Einstein equation to study classical gravity coupled to a quantum scalar field with potential in spherical symmetry. The system is defined by effective constraints where the matter terms are…

We introduce an Allen-Cahn type functional, $\text{BE}_{\epsilon}$, that defines an energy on separating hypersurfaces, $Y$, of closed Riemannian Manifolds. We establish $\Gamma$-convergence of $\text{BE}_{\epsilon}$ to the area functional,…

First, we show that a warped product of a line and a fiber manifold is weakly conformally flat and quasi Einstein if and only if the fiber is Einstein. Next, we characterize and classify contact (in particular, $K$-contact) Riemannian…

Let $M^m$ be a compact oriented smooth manifold which admits a smooth circle action with isolated fixed points which are isolated as singularities as well. Then all the Pontryagin numbers of $M^m$ are zero and its Euler number is…

One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a…

Let M be a closed enlargeable spin manifold. We show non-triviality of the universal index obstruction in the K-theory of the maximal $C^*$-algebra of the fundamental group of M. Our proof is independent from the injectivity of the…

We discuss vacuum static, spherically symmetric asymptotically flat solutions of the generalized hybrid metric-Palatini theory of gravity (generalized HMPG) suggested by B\"ohmer and Tamanini, involving both a metric $g_{\mu\nu}$ and an…

Reflection in a line in Euclidean 3-space defines an almost paracomplex structure on the space of all oriented lines, isometric with respect to the canonical neutral Kaehler metric. Beyond Euclidean 3-space, the space of oriented geodesics…

In [Comm. Anal. Geom., 13(5):845-885, 2005.], Bartnik described the phase space for the Einstein equations, modelled on weighted Sobolev spaces with local regularity $(g,\pi)\in H^2\times H^1$. In particular, it was established that the…

We use some natural lifts defined on the cotangent bundle T*M of a Riemannian manifold (M,g) in order to construct an almost Hermitian structure (G,J) of diagonal type. The obtained almost complex structure J on T*M is integrable if and…

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the…

We consider the Einstein-Gauss-Bonnet gravity with a negative cosmological constant together with a source given by a scalar field nonminimally coupled in arbitrary dimension D. For a certain election of the cosmological and Gauss-Bonnet…

In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$.…

In 2002 Polterovich has notably established that on closed aspherical symplectic manifolds, Hamiltonian diffeomorphisms of finite order, which we call Hamiltonian torsion, must in fact be trivial. In this paper we prove the first…

On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is…

Suppose $X^{N}$ is a closed oriented manifold, $\alpha \in H^*(X;\mathbb{R})$ is a cohomology class, and $Z \in H_{N-k}(X)$ is an integral homology class. We ask the following question: is there an oriented embedded submanifold $Y^{N-k}…

We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with…

The paper provides computations of the first non-vanishing $\mathbb{A}^1$-homotopy sheaves of the orthogonal Stiefel varieties which are relevant for the unstable isometry classification of quadratic forms over smooth affine schemes over…

This paper is about non-holomorphic isometric immersions of Kaehler manifolds into Euclidean space $f\colon M^{2n}\to\R^{2n+p}$, $p\leq n-1$, with low codimension $p\leq 11$. In particular, it addresses a conjecture proposed by J. Yan and…

Riemannian Manifolds may be $C^{1,1}$ and the geometry of these manifolds is investigated in \cite{Groah1}. Here, a similar analysis is given for pseudohermitian, torsion-free manifolds whereby, instead of assuming that the metric is…