A
series of the most remarkable results in mathematics are related to Grisha
Perelman’s proof of the Poincare Conjecture built on geometrization (Thurston)
conjecture for three dimensional
Riemannian manifolds, and R. Hamilton’s Ricci flow theory see reviews and basic references explained by Kleiner. Much of the works on Ricci flows has been
performed and validated by experts in the area of geometrical analysis and
Riemannian geometry. Recently, a number of applications in physics of the Ricci
flow theory were proposed, by Vacaru.
Some geometrical approaches in modern
gravity and string theory are connected to the method of moving frames and
distributions of geometric objects on (semi) Riemannian manifolds and their
generalizations to spaces provided with nontrivial torsion, nonmetricity and/or
nonlinear connection structures. The geometry of nonholonomic manifolds and non–Riemannian spaces is largely applied in modern mechanics, gravity,cosmology and classical/quantum field theory explained by Stavrinos.
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