Solvability and bifurcations of some strongly nonlinear equations
We present some comments on the diversity of the paintings by Johannes Vermeer (1632-1675) depicted on postage stamps. We have found 20 of the 36 "recognized" Vermeer paintings depicted on postage stamps issued by 29 "countries"; by country we mean here a stamp-issuing region that issues or has issued its own postage stamps. We apply Fisher's α index of biodiversity [11] to compare the diversity of Vermeer paintings depicted on postage stamps with the diversity of two other data sets [26]. We illustrate...
The author obtains the classification of all invariant Einstein metrics on the following homogeneous spaces: , , , . Combining this with the results of other authors, the classification of all invariant Einstein metrics on all compact simply connected homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature is obtained.
Given a fibered manifold , a 2-connection on means a section . The authors determine all first order natural operators transforming a 2-connection on and a classical linear connection on into a connection on . (The proof implies that there is no first order natural operator transforming 2-connections on into connections on .) Using this result, the authors deduce several properties of characterizable connections on .