Eta invariant and Selberg zeta function of odd type over convex co-compact hyperbolic manifolds
نویسندگان
چکیده
منابع مشابه
Eta Invariants and Regularized Determinants for Odd Dimensional Hyperbolic Manifolds with Cusps
We study eta invariants of Dirac operators and regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner Müller (see [18], [19]) and use relative traces to define the eta function and the zeta function. We show regularities of eta and zeta functions at the origin so that we can define the eta invariant and the regularized determinant. By the Selberg tra...
متن کاملHyperbolic manifolds with convex boundary
Let (M,∂M) be a 3-manifold, which carries a hyperbolic metric with convex boundary. We consider the hyperbolic metrics on M such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature K > −1, and that the third fundamental forms of ∂M are exactly the metrics with curvature K < 1, for which closed geodesics which a...
متن کاملCompact Hyperbolic 4-manifolds of Small Volume
We prove the existence of a compact non-orientable hyperbolic 4-manifold of volume 32π2/3 and a compact orientable hyperbolic 4-manifold of volume 64π2/3, obtainable from torsion-free subgroups of small index in the Coxeter group [5, 3, 3, 3]. At the time of writing these are the smallest volumes of any known compact hyperbolic 4-manifolds.
متن کاملThe Selberg Zeta Function and Scattering Poles for Kleiman Groups
In this note we present a polynomial bound on the distribution of poles of the scattering operator for the Laplacian on certain hyperbolic manifolds M of infinite volume. The motivation is to understand more fully the geometry of the poles of the scattering operator. The proof uses the relationship between poles of the scattering operator and zeros of the Selberg zeta function for geodesic flow...
متن کاملProperly Convex Bending of Hyperbolic Manifolds
In this paper we show that bending a finite volume hyperbolic d-manifold M along a totally geodesic hypersurface Σ results in a properly convex projective structure on M with finite volume. We also discuss various geometric properties of bent manifolds and algebraic properties of their fundamental groups. We then use this result to show in each dimension d Ê 3 there are examples finite volume, ...
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: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.05.004