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Spectral Geometry, Riemannian Submersions and the Gromov-lawson Conjecture / Edition 1
     

Spectral Geometry, Riemannian Submersions and the Gromov-lawson Conjecture / Edition 1

by Peter B. Gilkey
 

ISBN-10: 0849382777

ISBN-13: 9780849382772

Pub. Date: 07/27/1999

Publisher: Taylor & Francis

This cutting-edge, standard-setting text explores the spectral geometr y of Riemannian submersions. Working for the most part with the form v alued Laplacian in the class of smooth compact manifolds without bound ary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and p: Z (r)

Overview

This cutting-edge, standard-setting text explores the spectral geometr y of Riemannian submersions. Working for the most part with the form v alued Laplacian in the class of smooth compact manifolds without bound ary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on Z, given that Dp is the p form valued Laplacian and p: Z (r) Y is a Riemannian submersion.

Product Details

ISBN-13:
9780849382772
Publisher:
Taylor & Francis
Publication date:
07/27/1999
Series:
Studies in Advanced Mathematics Series , #30
Pages:
296
Product dimensions:
6.40(w) x 9.50(h) x 0.86(d)

Table of Contents

ELLIPTIC OPERATORS
Introduction
The Real and Complex Laplace Operators
Spinors
Spectral Resolutions
Manifolds with Boundary
Spectral Invariants
The Eta Invariant
Computing the Eta Invariant
DIFFERENTIAL GEOMETRY
Introduction
Riemannian Submersions
Characteristic Classes
The Geometry of Sphere and Principal Bundles
The Geometry of Circle Bundles
The Hopf Fibration
The Scalar Curvature
Levi-Civita and Spin Connections
POSITIVE CURVATURE
Introduction
Manifolds with Positive Ricci Curvature
Bordism and Connective K Theory
Calculations Involving the Eta Invariant
The Eta Invariant and Connective K Theory
Computing Connective K Theory Groups
SPECTRAL GEOMETRY OF RIEMANNIAN SUBMERSIONS
Introduction
Intertwining the Coderivitives
The Real Laplacian
The Complex Laplacian
The Spin Laplacian
Riemannian Submersions with Boundary
Heat Trace and Heat Content
Unresolved Questions
REFERENCES
Introduction
Main Bibliography
Bibliography of Harmonic Morphisms
Parabolic PDE Bibliography
NOTATION
INDEX

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