Related papers: Conformal equivalence between certain geometries i…

We construct new examples of non-formal simply connected compact Sasaki-Einstein 7-manifolds. We determine the minimal model of the total space of any fibre bundle over $CP^2$ with fibre $S^1\times S^2$ or $S^3/Z_p$ ($p>0$), and we apply…

We develop a new approach to the conformal geometry of embedded hypersurfaces by treating them as conformal infinities of conformally compact manifolds. This involves the Loewner--Nirenberg-type problem of finding on the interior a metric…

I use local differential geometric techniques to prove that the algebraic cycles in certain extremal homology classes in Hermitian symmetric spaces are either rigid (i.e., deformable only by ambient motions) or quasi-rigid (roughly…

We show that properties of hypergeometric type equations become transparent if they are derived from appropriate 2nd order partial differential equations with constant coefficients. In particular, we deduce the symmetries of the…

Almost para-quaternionic structures on smooth manifolds of dimension $2n$ are equivalent to almost Grassmannian structures of type $(2,n)$. We remind the equivalence and exhibit some interrelations between subjects that were previously…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

We reduce to various absolute parallelisms, namely to certain {e}-structures on manifolds of dimensions 7, 6, 5, the biholomorphic equivalence problem or the intrinsic CR equivalence problem for generic submanifolds M^5 in C^4 of CR…

Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static…

In this paper, we explore the similarity between normal homogeneity and $\delta$-homogeneity in Finsler geometry. They are both non-negatively curved Finsler spaces. We show that any connected $\delta$-homogeneous Finsler space is…

Any oriented $4$-dimensional Einstein metric with semi-definite sectional curvature satisfies the pointwise inequality \[ \frac{|s|}{\sqrt{6}}\geq|W^+|+|W^-|, \] where $s$, $W^+$ and $W^-$ are respectively the scalar curvature, the…

We study a two-dimensional dilaton gravity model related by a conformal transformation of the metric to the Callan-Giddings-Harvey-Strominger model. We find that most of the features and problems of the latter can be simply understood in…

We studied the axiom of anti-invariant 2-spheres and the axiom of co-holomorphic $(2n+1)$-spheres. We proved that a nearly K\"{a}hlerian manifold satisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional…

In this paper we study several aspects of the geometry of conformally stationary Lorentz manifolds, and particularly of GRW spaces, due to the presence of a closed conformal vector field. More precisely, we begin by extending to these…

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.

Let f be an integer greater than one. We study three progressively finer equivalence relations on closed 3-manifolds generated by Dehn surgery with denominator f: weak f-congruence, f-congruence, and strong f-congruence. If f is odd, weak…

We study hypersurfaces in a nearly $\mathrm{G}_2$ manifold. We define various quantities associated to such a hypersurface using the $\mathrm{G}_2$ structure of the ambient manifold and prove several relationships between them. In…

We survey different classification results for surfaces with parallel mean curvature immersed into some Riemannian homogeneous four-manifolds, including real and complex space forms, and product spaces. We provide a common framework for…

We study the infinitesimal deformations of a proper nearly parallel G_2-structure and prove that they are characterized by a certain first order differential equation. In particular we show that the space of infinitesimal deformations…

We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated.…

Let $(M,g_M,\mathcal F)$ be a closed, connected Riemannian manifold with a Riemannian foliation $\mathcal F$ of nonzero constant transversal scalar curvature. When $M$ admits a transversal nonisometric conformal field, we find some…