Parallel submanifolds with an intrinsic product structure

Let $M$ and $N$ be Riemannian symmetric spaces and $f:M\to N$ be a parallel isometric immersion. We additionally assume that there exist simply connected, irreducible Riemannian symmetric spaces $M_i$ with $\dim(M_i)\geq 2$ for $i=1,...,r$ such that $M\cong M_1\times...\times M_r$ . As a starting point, we describe how the intrinsic product structure of $M$ is reflected by a distinguished, fiberwise orthogonal direct sum decomposition of the corresponding first normal bundle. Then we consider the (second) osculating bundle \osc f, which is a $\nabla^N$-parallel vector subbundle of the pullback bundle $f^*TN$, and establish the existence of $r$ distinguished, pairwise commuting, $\nabla^N$-parallel vector bundle involutions on \osc f . Consequently, the "extrinsic holonomy Lie algebra" of \osc f bears naturally the structure of a graded Lie algebra over the Abelian group which is given by the direct sum of $r$ copies of $\Z/2 \Z$ . Our main result is the following: Provided that $N$ is of compact or non-compact type, that $\dim(M_i)\geq 3$ for $i=1,...,r$ and that none of the product slices through one point of $M$ gets mapped into any flat of $N$, we can show that $f(M)$ is a homogeneous submanifold of $N$ .Comment: 25 pages, Appendix A added, a few corrections, new numbering of the theorem

Capital inflows and asset prices: evidence from emerging Asia : [Version 4 September 2012]

The withdrawal of foreign capital from emerging countries at the height of the recent financial crisis and its quick return sparked a debate about the impact of capital flow surges on asset markets. This paper addresses the response of property prices to an inflow of foreign capital. For that purpose we estimate a panel VAR on a set of Asian emerging market economies, for which the waves of inflows were particularly pronounced, and identify capital inflow shocks based on sign restrictions. Our results suggest that capital inflow shocks have a significant effect on the appreciation of house prices and equity prices. Capital inflow shocks account for - roughly - twice the portion of overall house price changes they explain in OECD countries. We also address crosscountry differences in the house price responses to shocks, which are most likely due to differences in the monetary policy response to capital inflows