Related papers: A generalized integrability problem for G-Structur…

For any compact Lie group $G$ and any $n$ we construct a smooth $G$-manifold $U_n(G)$ such that any smooth $n$-dimensional $G$-manifold can be embedded in $U_n(G)$ with a trivial normal bundle. Furthermore, we show that such embeddings are…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

A statistical structure $(g, T)$ on a smooth manifold $M$ induced by $(\tilde M, \tilde g, \tilde T)$ is said to be {\em robust} if there exists an open neighborhood of $(g,T)$ in the fine $C^{\infty}$-topology consisting of statistical…

We develop various properties of symmetric generalized complex structures (in connection with their holomorphic space and B-field transformations), which are analogous to the well-known results of Gualtieri on skew-symmetric generalized…

We prove that for an induced CR structure on a compact, generic, regular 3-pseudoconcave CR submanifold ${\bold M}\subset{\bold G}$, of a complex manifold ${\bold G}$, satisfying condition $\dim H^1({\bold M}, T^{\prime}({\bold G})|_{\bold…

We investigate the geometry and topology of compact submanifolds of arbitrary codimension in space forms satisfying a certain pinching condition involving the length of the second fundamental form and the mean curvature. We prove that this…

In this paper we define the notion of a generalized coK\"ahler structure and prove that the product $M_{1}\times M_{2}$ of generalized contact metric manifolds $(M_i, \Phi_i,E_{\pm,i}, G_i)$, $ i=1, 2$, where $M_{1}\times M_{2}$ is endowed…

In this paper, we study some aspects of the irreducibility of $\widetilde{M_g^{Pl}(G)}$ and its interrelation with the existence of "normal forms", i.e. non-singular plane equations (depending on a set of parameters) such that a…

This paper is concerned with the geometry of the moduli space $\mathscr{M}$ of torsion-free $G_2$-structures on a compact $G_2$-manifold $M$, equipped with the volume-normalised $L^2$-metric $\mathscr{G}$. When $b^1(M) = 0$, this metric is…

An integral geometric curvature is defined as the index expectation K(x) = E[i(x)] if a probability measure m is given on vector fields on a Riemannian manifold or on a finite simple graph. Such curvatures are local, satisfy Gauss-Bonnet…

We study complete noncompact long time solutions $(M, g(t))$ to the K\"ahler-Ricci flow with uniformly bounded nonnegative holomorphic bisectional curvature. We will show that when the Ricci curvature is positive and uniformly pinched, i.e.…

In the context of generalised geometry we investigate reductions to $SU(m)\times SU(m)$ together with an integrability condition which in dimension 6 describes the geometry of type II supergravity compactifications.

Let $g$ be locally homogeneous (LH) Riemannian metric on a differentiable compact manifold $M$, and $K$ be a compact Lie group endowed with an $\mathrm {ad}$-invariant inner product on its Lie algebra $\mathfrak{k}$. A connection $A$ on a…

We study a relationship between regular flat structures and generalized Okubo systems. We show that the space of variables of isomonodromic deformations of a regular generalized Okubo system can be equipped with a flat structure. As its…

We study homomorphisms of locally compact quantum groups from the point of view of integrability of the associated action. For a given homomorphism of quantum groups $\Pi\colon\mathbb{H}\to\mathbb{G}$ we introduce quantum groups…

We expand upon a claim made in a recent paper [arXiv:1411.5721] that generic minimally supersymmetric AdS backgrounds of warped flux compactifications of Type II and M theory can be understood as satisfying a straightforward weak…

Let $\widetilde{\mathcal M}=\langle \mathcal M, G\rangle$ be an expansion of a real closed field $\mathcal M$ by a dense subgroup $G$ of $\langle M^{>0}, \cdot\rangle$ with the Mann property. We prove that the induced structure on $G$ by…

In this paper we will show that the generalized connected sum construction for constant scalar curvature metrics can be extended to the zero scalar curvature case. In particular we want to construct solutions to the Yamabe equation on the…

Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…

Let $M$ be a 3-manifold. Every knotted (embedded) surface in $M \times \R$ can be moved via an ambient isotopy in such a way that its projection into $M$ is a generic surface. A surface is generic if every point on it is either a regular,…