Related papers: Compactness of Dirac-Einstein spin manifolds and h…

In this paper we compute the first and second variation of the normalized Einstein-Hilbert functional on CR manifolds. We characterize critical points as pseudo-Einstein structures. We then turn to the second variation on standard spheres.…

We characterize the set of all conformal Spin(7) forms on an oriented and spin Riemannian eight-manifold $(M,g)$ as solutions to a homogeneous algebraic equation of degree two for the self-dual four-forms of $(M,g)$. When $M$ is compact, we…

The eta invariant appears regularly in index theorems but is known to be directly computable from the spectrum only in certain examples of locally symmetric spaces of compact type. In this work, we derive some general formulas useful for…

We study critical metrics of higher-order curvature functionals on compact Riemannian $n$-manifolds $(M,g)$. For an integer $k$ with $2 \leq 2k \leq n$, let $R^k$ denote the $k$-th exterior power of the Riemann curvature tensor. We…

We continue our study of the mixed Einstein-Hilbert action as a functional of a pseudo-Riemannian metric and a linear connection. Its geometrical part is the total mixed scalar curvature on a smooth manifold endowed with a distribution or a…

We study a variational problem on a smooth manifold with a decomposition of the tangent bundle into $k>2$ subbundles (distributions), namely, we consider the integrated sum of their mixed scalar curvatures as a functional of adapted…

For compact submanifolds in Euclidean and Spherical space forms with Ricci curvature bounded below by a function $\alpha(n,k,H,c)$ of mean curvature, we prove that the submanifold is either isometric to the Einstein Clifford torus, or a…

Let $(M,g)$ be a closed Riemannian spin manifold. The constant term in the expansion of the Green function for the Dirac operator at a fixed point $p\in M$ is called the mass endomorphism in $p$ associated to the metric $g$ due to an…

As a commutative version of the supersymmetric nonlinear sigma model, Dirac-harmonic maps from Riemann surfaces were introduced fifteen years ago. They are critical points of an unbounded conformally invariant functional involving two…

We re-visit the eigenvalue estimate of the Dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal Laplace operator as well as the conformal mean curvature operator. These problems were studied earlier…

In this note, we look at estimates for the scalar curvature k of a Riemannian manifold M which are related to spin^c Dirac operators: We show that one may not enlarge a Kaehler metric with positive Ricci curvature without making k smaller…

We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat…

We classify Einstein metrics on $\mathbb{R}^4$ invariant under a four-dimensional group of isometries including a principal action of the Heisenberg group. The metrics are either Ricci-flat or of negative Ricci curvature. We show that all…

We consider the dynamics of Dirac particles moving in the curved spaces with one coordinate subjected to compactification and thus interpolating smoothly between three- and two-dimensional spaces. We use the model of compactification, which…

This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact manifolds; on asymptotically Euclidean manifolds, the…

The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$…

A new concept of geometrization of electromagnetic field is proposed. Instead of the concept of extended field and its point sources, the interacting Maxwellian and Dirac electron--positron fields are considered as a microscopic unified…

We study critical metrics of the curvature functional $\A(g)=\int_M |R|^2\, \vol$, on complete four-dimensional Riemannian manifolds $(M,g)$ with finite energy, that is, $\A(g)<\infty$. Under the natural inequality condition on the…

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with…

In this article we present the algebraic rearrangement, or matrix inversion of the Dirac equation in a curved Riemann-Cartan spacetime with torsion, the presence of non-vanishing torsion is implied by the intrinsic spin-1/2 of the Dirac…