With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assump…
This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi equation which, through discussion of tidal forces, further helps motivate the Einstein…
Most of the methods described in this book can be used with cosmetic modifications to solve transfer problems of greater complexity. All attempts have been made to make the book self-contained.
Metric Foliations and Curvature
by Gromoll, Detlef, Walschap, Gerard
fromProgress in Mathematics Ser
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