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The geometry of physics : an introduction
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The Geometry of Physics
Preface Part I. Manifolds, Tensors and Exterior Forms: 1. Manifolds and vector fields 2. Tensors and exterior forms 3. Integration of differential forms 4. The Lie derivative 5. The Poincare Lemma
THE LEFSCHETZ THEOREM ON HYPERPLANE SECTIONS
is bijective for i < n - 1 and surjective for i = n - 1. Several proofs of this theorem are to be found in the literature (see [5] for an account of the problem). Recently Thom has given a proof
Fixed Points and Torsion on Kahler Manifolds
When a 1-parameter group acts by isometries on a Riemannian manifold M, the fixed point set F is nicely behaved. It is known that each component Fo0 of F is a totally geodesic submanifold of M whose
Maxwell's Equations
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