On the spectrum of homogeneous spherical space forms
نویسندگان
چکیده
منابع مشابه
ON h-COBORDISMS OF SPHERICAL SPACE FORMS
Given a manifold M of dimension at least 4 whose universal covering is homeomorphic to a sphere, the main result states that a compact manifold W is isomorphic to a cylinder M × [0, 1] if and only if W is homotopy equivalent to this cylinder and the boundary is isomorphic to two copies of M ; this holds in the smooth, PL and topological categories. The result yields a classification of smooth, ...
متن کاملSpherical Space Forms Revisited
We give a simplified proof of J. A. Wolf’s classification of finite groups that can act freely and isometrically on a round sphere of some dimension. We slightly improve the classification by removing some non-obvious redundancy. The groups are the same as the Frobenius complements of finite group theory. In chapters 4–7 of his famous Spaces of Constant Curvature [7], J. A. Wolf classified the ...
متن کاملSpherical Minimal Immersions of Spherical Space Forms
Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator on M for the same eigenvalue. And conve...
متن کاملTopological Spherical Space Forms
Free actions of finite groups on spheres give rise to topological spherical space forms. The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. In this article, we present a survey of some of the main results and a guide to the literature.
متن کاملIsospectrality for Spherical Space Forms
Consider the set S(q,r) of isometry classes of q-dimensional spherical space forms whose fundamental groups are isomorphic to a fixed group r. We define a certain group A(q, r) of transformations on the finite set S(q, r), prove that any two elements in the same A(q, r)-orbit are strongly isospectral, and study some consequences. Then a number of the results are carried over to riemannian quoti...
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: Kodai Mathematical Journal
سال: 1995
ISSN: 0386-5991
DOI: 10.2996/kmj/1138043353