Invariance Theory Heat Equation and Atiyah Singer Index Theorem
Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic…
The spectral geometry of a Riemannian manifold
- P. Gilkey
- Mathematics
- 1975
We adopt the convention of summing over repeated indices except where otherwise indicated. Let (g) denote the inverse of the matrix (g^ ). Let V be a smooth vector bundle over M and let D be a second…
Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor
- P. Gilkey
- Mathematics
- 1 November 2001
Algebraic curvature tensors the skew-symmetric curvature operator the Jacobi operator controlling the eigenvalue structure.
Asymptotic Formulae in Spectral Geometry
- P. Gilkey
- Mathematics
- 17 December 2003
A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects…
The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds
- P. Gilkey
- Mathematics
- 26 April 2007
The Geometry of the Riemann Curvature Tensor Curvature Homogeneous Generalized Plane Wave Manifolds Other Pseudo-Riemannian Manifolds The Curvature Tensor Complex Osserman Algebraic Curvature Tensors…
The asymptotics of the Laplacian on a manifold with boundary
- T. Branson, P. Gilkey, Dmitri V.Vassilevich
- Mathematics
- 6 April 1995
Let P be a second-order differential operator with leading symbol given by the tensor on a compact Riemannian manifold with boundary. We compute the asymptotics of the heat equation for Dirichlet,…
Residues of the eta function for an operator of Dirac type
- T. Branson, P. Gilkey
- Mathematics
- 15 August 1992
On the Index of Geometrical Operators for Riemannian-Manifolds with Boundary
- P. Gilkey
- Mathematics
- 1 December 1993
Abstract We use heat equation methods and invariance theory to compute the index of the classical elliptic complexes with pseudo-differential boundary conditions of Atiyah-Patodi-Singer type where…
Some representations of exceptional Lie algebras
In this note, we give the dimensions of some irreducible representations of exceptional Lie algebras and algebraic groups. Similar results appear in [1] for classical groups and algebras of rank at…
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