Curvature properties of exotic spheres

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== Introduction ==

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