Ricci solitons and odd-dimensional spheres
The reviewed paper is concerned with characterizations of a standard sphere. Let \(M\) be an isometrically immersed oriented real hypersurface in a complex space \(\mathbb C^n\) with a flat Kähler structure \((J,\tilde g)\). The Reeb vector field \(\xi\) is defined by \(\xi=-JN\), where \(N\) is a unit normal vector field on \(M\). The author gives two sufficient conditions (inequalities in terms of the shape operator, the Reeb vector field and its associated 1-form) for a compact real hypersurface \(M\) in \(\mathbb C^n\) to be a standard sphere. Moreover, he proves that, if such an \(M\) admits a Ricci soliton whose potential vector field is the Reeb vector field, then \(M\) is a sphere.
scientific article; zbMATH DE number 5764652