Related papers: Uplifting the Iwasawa
We investigate the existence of strong K\"ahler with torsion metrics along deformations of the Iwasawa manifold and of the holomorphically parallelizable Nakamura manifold. We also show that the class of deformations of the holomorphically…
We develop a general deformation principle for families of Riemannian metrics on smooth manifolds with possibly non-compact boundary, preserving lower scalar curvature bounds. The principle is used in order to strengthen boundary…
We consider holographic RG flow solutions with eight supersymmetries and study the geometry transverse to the brane. For both M2-branes and for D3-branes in F-theory this leads to an eight-manifold with only a four-form flux. In both…
We investigate the viability of predictive schemes for quark-lepton Yukawa ratios and nucleon decay in non-supersymmetric SU(5) Grand Unified Theories (GUTs) where neutrino masses are generated by a type II seesaw mechanism. The scalar…
We study 8-dimensional Riemannian manifolds that admit a PSU(3)-structure. We classify these structures by their intrinsic torsion and characterize the corresponding classes via differential equations. Moreover, we consider a connection…
For a RS model, with SM fields in the bulk and the Higgs boson on the TeV-brane, we suggest two specific structures for the Yukawa couplings, one based on a permutation symmetry and the other on the Universal Strength of Yukawa couplings…
We give a new, connected-sum-like construction of Riemannian metrics with special holonomy G_2 on compact 7-manifolds. The construction is based on a gluing theorem for appropriate elliptic partial differential equations. As a prerequisite,…
We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory…
Let $M$ be a 5 dimensional Riemannian manifold with $Sec_M\in[0,1]$, $\Sigma$ be a locally conformally flat hypersphere in $M$ with mean curvature $H$. We prove that, there exists $\varepsilon_0>0$, such that $\int_\Sigma (1+H^2)^2 \ge…
In this work we give a detailed description of Matthias G\"unther's proof of the Isometric Embedding Theorem of Riemannian manifolds. Subsequently we will use this method to show that it is possible to construct an isometric embedding of a…
We present exact solutions of four-dimensional Einstein's equations related to Minkoswki vacuum constructed from Type IIB string theory with non-trivial fluxes. Following recent works, we study a non-trivial flux compactification on a…
In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in Finsler manifolds and give the necessary and sufficient conditions for a transnormal function to be isoparametric. We then prove that hyperplanes,…
In this paper, we establish the existence of conformal deformations that uniformize fourth order curvature on 4-dimensional Riemannian manifolds with positive conformal invariants. Specifically, we prove that any closed, compact Riemannian…
The aim of this article is to study the geometry of Bott-Chern hypercohomology from the bimeromorphic point of view. We construct some new bimeromorphic invariants involving the cohomology for the sheaf of germs of pluriharmonic functions,…
The twistor space of a Riemannian 4-manifold carries two almost complex structures, $J_+$ and $J_-$, and a natural closed 2-form $\omega$. This article studies limits of manifolds for which $\omega$ tames either $J_+$ or $J_-$. This amounts…
In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional sigma models on special holonomy manifolds have extra symmetries that are in one-to-one correspondence with the covariantly constant forms on these manifolds. The…
The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…
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…
In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\leq n+1\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. Suppose the union of non-principal orbits…
The group Spin(7) belongs to the list of possible holonomy of an eight-dimensional Riemannian manifold. The weaker notion of Spin(7)-structures plays for manifolds with holonomy Spin(7), the analogue of almost Hermitian for K{\"a}hler…