I am looking for generalizations of the following construction. Let $G$ be a connected, reductive group and let $\theta : G \rightarrow G$ be an involution. Let $H = G^{\theta}$ …

Let $G/H$ be a compact symmetric space. Then I believe the following is true: if $\alpha \in \Omega^k(G/H)$ and $\nabla$ the Levi-Civita connection, then $$ (\alpha \text{ is ind …

I am reading the paper "Ricci-flat metrics on the complexification of a compact rank one symmetric space" by Stenzel (here is the link:"http://www.math.osu.edu/~stenzel.3/research/ …

Hallo, I have a question on a paper of Azad and Kobayashi "Ricci-flat Kähler metrics on symmetric varieties". Here is the link: http://www.academia.edu/2579043/Ricci-flat_Kahler_m …

My question is the following : Given an algebraic curvature operator $R\in S^2_B(\Lambda^2\mathbb{R}^n)$, is there an a simple criterion to know if this curvature operator can …

Maskit's combination theorem says: if $M=M_1\cup_\Sigma M_2$ is a union of hyperbolic 3-manifolds $M_1=\Gamma_1\backslash H^3, M_2=\Gamma_2\backslash H^3$ along a surface $\Sigma$, …

Let $G$ be a simply connected complex Lie group, $\theta$ an involution, and $K = G^\theta$ the fixed point subgroup. Pick a $\theta$-invariant Borel subgroup $B$. Then there is a …

The collection of marked unimodular lattices in the euclidean $n$-space corresponds to the symmetric space $S_n:=SO_n(\mathbb{R}) \backslash SL_n(\mathbb{R})$. I have only recent …

Let $G$ be a complex connected reductive Lie group, $\theta$ an involution, and $K = G^\theta$ the fixed-point subgroup. Then $K$ has finitely many orbits on $G/B$, one of which i …

I want to compare the two canonical volume forms on a noncompact symmetric space fo real rank one. The first one is the volume form induced by the Riemannian structure given by th …

There is a well-known duality between compact symmetric spaces and symmetric spaces of noncompact type. Basically it goes as follows: If $G/K$ is a symmetric space of noncompact ty …

During my research I have recently stumbled upon the problem of finding the relative homotopy sets $\pi_1(U_n,U_n/O_n)$ and $\pi_1(U_{2n},U_{2n}/USp_{2n})$ for $n$ large enough to …

Here by riemannian symmetric domain is understood an riemannian symmetric space with only factors of non-compact types. Such domains are realized as quotients of the form $D=G/K$, …

A Hermitian symmetric space is a connected complex manifold with a hermitian metric on which the group of holomorphic isometries acts transitively, and which satisfies the followin …

Recall the list of irreducible simply connected inner symmetric spaces of compact type in dimension $4k+2$: Hermitian symmetric spaces (one can write them down explicitly); Grass …