相关论文: A new class of austere submanifolds

In 2015, Archdeacon proposed the notion of Heffter arrays in view of its connection to several other combinatorial objects. In the same paper he also presented the following variant. A weak Heffter array $\mathrm{W}\mathrm{H}(m,n;h,k)$ is…

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…

In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral superfields. Starting from the two necessary…

This article sets out to serve a dual purpose. On the one hand, we give an explicit description of the Lagrangian submanifolds of the nearly Kaehler 6-sphere which are ruled by circles of constant radius using Weierstrass formulae. On the…

In this paper we study the scalar geometries occurring in the dimensional reduction of minimal five-dimensional supergravity to three Euclidean dimensions, and find that these depend on whether one first reduces over space or over time. In…

Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant…

The existing classification of homogeneous quaternionic spaces is not complete. We study these spaces in the context of certain $N=2$ supergravity theories, where dimensional reduction induces a mapping between {\em special} real, K\"ahler…

The monograph offers a coherent and self-contained treatment of massless (ladder) representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2), combining rigorous representation-theoretic analysis with…

We develop a theory of stable bundles and affine Hermitian-Einstein metrics for flat vector bundles over a special affine manifold (a manifold admitting an atlas whose gluing maps are all locally constant volume-preserving affine maps). Our…

We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian…

We establish a coordinate-invariant Heisenberg-type lower bound for quantum states strictly localized in geodesic balls of radius $r_g$ on horizon-regular spacelike slices of static, spherically symmetric, asymptotically flat (AF)…

The paper presents a generalized Weierstrass representation for pseudospherical surfaces in terms of 3x3 matrices, using moving frames and loop group decompositions. The construction of all such surfaces, starting from a given…

Minimal surfaces of general type in Euclidean 4-space are characterized with the conditions that the ellipse of curvature at any point is centered at this point and has two different principal axes. Any minimal surface of general type…

The notions of weakly bipartitive and bipartitive families were introduced by Montgolfier (2003) as a general tool for studying some decomposition of graphs and other combinatorial structures. In this paper, we give a matrix description of…

Morse functions with exactly two singular points on spheres and canonical projections of spheres belong to the class of a certain good class of smooth maps: special generic maps. We mainly investigate information on cohomology of closed and…

We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and then show that it can produce many of the known minimal surfaces in $\mathbb{S}^3$ up to genus and symmetry group. We also produce several new infinite…

The construction of new hyper-Kaehler manifolds by taking the infinite monopole mass limit of certain Bogomol'nyi-Prasad-Sommerfield monopole moduli spaces is considered. The one-parameter family of hyperkaehler manifolds due to Dancer is…

We construct examples of non-isotrivial algebraic families of smooth complex projective curves over a curve of genus 2. This solves a problem from Kirby's list of problems in low-dimensional topology. Namely, we show that 2 is the smallest…

In this paper we construct an almost negatively $1/4$-pinched Riemannian metric on a class of compact manifolds recently discovered by Stover and Toledo in [17]. It is known that these manifolds are K\"{a}hler and not locally symmetric.…