Curvature properties of exotic spheres

Revision as of 14:19, 7 June 2010

1 Introduction

This page is in the construction process!!!

A homotopy sphere of dimension $<!-- COMMENT: To achieve a unified layout, along with using the template below, please OBSERVE the following: besides, $...$ and $$...$$, you should use two environments: - For statements like Theorem, Lemma, Definition etc., use e.g. {{beginthm|Theorem 1|(Milnor)}} ... ... ... {{endthm}}. - For references, use e.g. {{cite|Milnor1958b}}. DON'T FORGET TO ENTER YOUR USER NAME INTO THE {{Authors| }} TEMPLATE BELOW. END OF COMMENT -->{{Authors|Joachim}} {{Stub}} == Introduction == <wikitex>; This page is in the construction process!!! A homotopy sphere of dimension $n$ is an oriented closed smooth manifold which is homotopy equivalent to the standard sphere $S^n$. A homotopy sphere is called an exotic sphere if it not diffeoemorphic to a standard sphere. General information about homotopy spheres (and exotic spheres) is given on [[Exotic spheres]]. One prominent question concerning the geometry of exotic spheres is: Given an exotic sphere, are there Riemannian metrics which fulfil specific positivity criteria? == Homotopy spheres with positive [[Wikipedia:Scalar curvature|sectional curvature]] == == Homotopy spheres with positive [[Ricci curvature]] == == Homotopy spheres with positive [[scalar curvature]] == </wikitex> == References == {{#RefList:}} [[Category:Theory]]n$ is an oriented closed smooth manifold which is homotopy equivalent to the standard sphere $S^n$. A homotopy sphere is called an exotic sphere if it not diffeoemorphic to a standard sphere. General information about homotopy spheres (and exotic spheres) is given on Exotic spheres.

One prominent question concerning the geometry of exotic spheres is: Given an exotic sphere, are there Riemannian metrics which fulfil specific positivity criteria?

1 Homotopy spheres with positive sectional curvature

2 Homotopy spheres with positive Ricci curvature

3 Homotopy spheres with positive scalar curvature

2 References