We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric. 1. Introduction Let (M n , g) be a smooth, closed Riemannian manifold of dimension n.
In this paper, based on the vector model for gravitational field we have found a metric tensor of the space –time that in the first order approximate it lead to the Schwarzschild metric tensor in the General Theory of Relativity(GTR).
This book is based on lectures delivered over the years by the author at the
Universit´e Pierre et Marie Curie, Paris, at the University of Stuttgart, and at
City University of Hong Kong. Its two-fold aim is to give thorough introductions
to the basic theorems of differential geometry and to elasticity theory in
The treatment is essentially self-contained and proofs are complete.
Institute for Theoretical Physics University of California Santa Barbara, CA 93106 email@example.com December 1997
Abstract These notes represent approximately one semester’s worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein’s equations, and three applications: gravitational radiation, black holes, and cosmology. Individual chapters, and potentially updated versions, can be found at http://itp.ucsb.edu/~carroll/notes/.
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