Lecture 2 | Introduction to Riemannian geometry, curvature and Ricci flow | John W. Morgan

Lecture 2 | Курс: Introduction to Riemannian geometry, curvature and Ricci flow, with applications to the topology of 3-dimensional manifolds | Лектор: John W. Morgan | Организатор: Математическая лаборатория имени П.Л.Чебышева
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[@robertgilmore1655]

[ The standard result I think is : D det A =( det A) Tr( A^(-1) D A) where D is the time derivative , A is a time function and A^(-1) is the inverse of matrix A]

[@ricci1729]

This is the 2nd lecture: Introduction to Riemannian geometry

[@robertgilmore1655]

Dear Prof Morgan, thank you very much for your nice lectures. I have a doubt : when you compute the time derivative of Vol(U) (under a Ricci flow), and apply an standard result for the time derivative of the determinant of the metric g (about minute 48 of the video), there is not an inverse of matrix g factor missing inside the Trace? Thank you.
[the standard formula I think is:
D det A(t) = det A(t) Tr(A^(-1) D A(t))
where D is the time derivative and A^(-1) is the inverse of the A matrix )

[@HotPepperLala]

Where is lecture 3?