On spherical space forms which are isospectral but not isometric

Orbifold Lens Spaces That Are Isospectral but Not Isometric

We answer Mark Kac’s famous question [K], “can one hear the shape of a drum?” in the negative for orbifolds that are spherical space forms. This is done by extending the techniques developed by A. Ikeda on Lens Spaces to the orbifold setting. Several results are proved to show that with certain restrictions on the dimensionalities of orbifold Lens spaces we can obtain infinitely many pairs of i...

Zk 2-MANIFOLDS ARE ISOSPECTRAL ON FORMS.

Multilinear forms which are products of linear forms

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

Spherical 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 ...

Topological 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.