Locally symmetric Einstein-Kaehler manifolds and spectral geometry
نویسندگان
چکیده
منابع مشابه
Locally symmetric submanifolds lift to spectral manifolds
In this work we prove that every locally symmetric smooth submanifoldM of Rn gives rise to a naturally defined smooth submanifold of the space of n × n symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs toM. We also present an explicit formula for the dimension of the spectral manifold in terms of the dimension and the intrinsic ...
متن کاملThe Spectral Geometry of Einstein Manifolds with Boundary
Let (M, g) be a compact Einstein manifold with smooth boundary. Let ∆p,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec(∆p,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.
متن کاملCounting Locally Symmetric Manifolds
We give quantitive estimates for the number of locally symmetric spaces of a given type with bounded volume. Explicitly, let S be a symmetric space of non-compact type without Euclidean de Rham factors. Then, after rescaling appropriately the Riemannian metric, the following hold. Theorem A If rank(S) = 1 and S ≇ H2,H3, then there are at most V V Riemannian manifolds, locally isometric to S, wi...
متن کاملIsospectral locally symmetric manifolds
In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-polynomial. Finally, we construct pairs of infinite towers of finite covers of a...
متن کاملEinstein Manifolds and Contact Geometry
We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1979
ISSN: 0040-8735
DOI: 10.2748/tmj/1178229843