Related papers: A moduli curve for compact conformally-Einstein K\…

For a sequence of extrinsic or intrinsic biharmonic maps $u_j: M_j\rightarrow N$ from a sequence of non-collapsed degenerating closed Einstein 4-manifolds $(M_j,g_j)$ with bounded Einstein constants, bounded diameters and bounded $L^2$…

If $M$ is the underlying smooth oriented $4$-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics $h$ on $M$ such that $W^+(\omega , \omega )> 0$, where $W^+$ is the self-dual Weyl curvature of $h$, and $\omega$ is a…

All hyperK\"ahler ALE 4-manifolds with a given non-trivial finite group $\Gamma$ in $SU(2)$ at infinity are parameterized by an open dense subset of a real linear space of dimension $3$rank$\Phi$. Here, $\Phi$ denotes the root system…

We show that if a compact connected $n$-dimensional manifold $M$ has a conformal class containing two non-homothetic metrics $g$ and $\tilde g=e^{2\varphi}g$ with non-generic holonomy, then after passing to a finite covering, either $n=4$…

We prove that any compact selfdual Einstein 4-orbifold of positive scalar curvature whose isometry group contains a 2-torus is, up to an orbifold covering, a quaternion Kaehler quotient of (k-1)-dimensional quaternionic projective space by…

Let $(\Sigma,\tau)$ denote a Riemann surface of genus $g \geq 2$ equipped with an anti-holomorphic involution $\tau$. In this paper we study the topology of the moduli space $M(r,\xi)^\tau$ of stable Real vector bundles over $(\Sigma,\tau)$…

In $\mathrm{PU}(2,1)$, the group of holomorphic isometries of the complex hyperbolic plane, we study the space of involutions $R_1, R_2, R_3, R_4, R_5$ satisfying $R_5R_4R_3R_2R_1=1$, where $R_1$ is a reflection in a complex geodesic and…

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…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant…

The classification of homogeneous quaternionic manifolds has been done by Alekseevskii, Wolf et al using transitive solvable group of isometries. These manifolds are not generically symmetric, but there is a subset of quaternionic manifolds…

We study invariant Einstein metrics on the indicated homogeneous manifolds $M$, the corresponding algebraic Einstein equations $E$, the associated with $M$ and $E$ Newton polytopes $P(M)$, and the integer volumes $\nu = \nu(P(M))$ of it…

Every compact K\"ahler manifold with negative first Chern class admits a unique metric $g$ such that $\text{Ric}(g) = -g$. Understanding how families of these metrics degenerate gives insight into their geometry and is important for…

For a closed smooth manifold $M$ admitting a symplectic structure, we define a smooth topological invariant $Z(M)$ using almost-K\"ahler metrics, i.e. Riemannian metrics compatible with symplectic structures. We also introduce $Z(M,…

We consider the moduli space MN of flat unitary connections on an open Kaehler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection and L2 cohomologies with…

Positive curvature and bosons Compact positive curvature Riemannian manifolds M with symmetry group G allow Conner-Kobayashi reductions M to N, where N is the fixed point set of the symmetry G. The set N is a union of smaller-dimensional…

We show that conformal manifolds in $d\geq 3$ conformal field theories with at least 4 supercharges are K\"ahler-Hodge, thus extending to 3d ${\cal N}=2$ and 4d ${\cal N}=1$ similar results previously derived for 4d ${\cal N}=2$ and ${\cal…

For a stable curve of genus $g\geq 2$ and simple Lie algebra of type A or C, we show that the conformal blocks algebra $\mathcal{A}$ on $\overline{\mathcal{M}}_g$ is finitely generated and establish an explicit connection to Schmitt and…

In this paper we first show that on projective manifolds (M, {\omega}), there are holomorphic determinant bundles (in the sense of Knusden-Mumford used by Bismut, Gillet, Soule) which play the role of the geometric quantum bundle, namely…

This paper aims to study the $(m,\rho)$-quasi Einstein manifold. This article shows that a complete and connected Riemannian manifold under certain conditions becomes compact. Also, we have determined an upper bound of the diameter for such…