Related papers: On the rigidity of the complex Grassmannians
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
We study a closed differential form on the symmetric space of positive definite matrices, which is defined using the Pfaffian and is $\mathsf{GL}_{2n}(\mathbb{Z})$ invariant up to a sign. It gives rise to an infinite family of unstable…
Gauge invariant treatments of the second order cosmological perturbation in a four dimensional homogeneous isotropic universe filled with the perfect fluid are completely formulated without any gauge fixing. We derive all components of the…
High-accuracy gravitational-wave modeling demands going beyond linear, first-order perturbation theory. Particularly motivated by the need for second-order perturbative models of extreme-mass-ratio inspirals and black hole ringdowns, we…
In the D-modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf O by a morphism. A major theorem says that these systems have only regular singularities. This paper examines the irregularity of an…
We provide an intrinsic formulation of the noncommutative differential geometry developed earlier by Chaichian, Tureanu, R. B. Zhang and the second author. This yields geometric definitions of covariant derivatives of noncommutative metrics…
Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…
We prove that every Riemann surface not isomorphic to the Riemann sphere admits an infinitesimal deformation of the complex structure. The proof is based in an investigation of the length of geodesics for the Kobayashi/Poincare metric.
We study general properties of holomorphic isometric embeddings of complex unit balls $\mathbb B^n$ into bounded symmetric domains of rank $\ge 2$. In the first part, we study holomorphic isometries from $(\mathbb B^n,kg_{\mathbb B^n})$ to…
Let $Q^*$ denote the dual of the quotient bundle on the Grassmannian $G(2,n)$. We prove that the ideal of $Q^*$ in its natural embedding has initial ideal equal to the Stanley-Reisner ideal of a certain unobstructed simplicial complex.…
Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant…
The integrability of the\ $\Lambda-$Einstein-nonlinear $SU(2)$ $\sigma$-model with nonvanishing cosmological charge is studied. We apply the method of singularity analysis of differential equations and we show that the equations for the…
We obtain a generic regularity result for stationary integral $n$-varifolds with only strongly isolated singularities inside $N$-dimensional Riemannian manifolds, in absence of any restriction on the dimension ($n\geq 2$) and codimension.…
We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of…
In this note we show that any real exact G-invariant (1,1)-form is the Ricci form of a Kaehler metric on the complexification of an irreducible compact symmetric space G/K.
The present article studies holomorphic isometric embeddings of arbitrary complex Grassmannians into quadrics, generalising results in [13]. The moduli spaces of these embeddings up to gauge and image equivalence are discussed using a…
This is the second in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…
Let (X,\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\"ahler class \Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative…
In this paper we discuss the dimensions of the (higher) secant varieties to the Grassmann varieties, embedded via the Plucker embeddings. We use Terracini's Lemma and the duality in the exterior algebra of a finite dimensional vector space…
We introduce a completely integrable system on the Grassmannian of 2-planes in an n-space associated with any triangulation of a polygon with n sides, and compute the potential function for its Lagrangian torus fiber. The moment polytopes…