Category Archives: Group theory

Hopf fibration double covers circle bundle of sphere

Two days ago, I gave a seminar talk on Chern‘s proof of the generalized Gauss-Bonnet theorem. Here I record the answer to a question asked by one of my colleague during the talk. Although not directly related to the proof … Continue reading

Posted in Algebra, Differential geometry, Group theory | Leave a comment

The Cauchy-Schwarz inequality and the Lagrange identity

The classical Lagrange identity is the following: This can be proven by expanding and separating the terms into the cross-terms part and the non cross-terms part. The Lagrange identity implies the Cauchy-Schwarz inequality in . And when , this can … Continue reading

Posted in Algebra, Group theory, Inequalities, Linear Algebra | Leave a comment