Universal curvature identities

We study scalar and symmetric 2-form valued universal curvature identities. We use this to establish the Gauss-Bonnet theorem using heat equation methods, to give a new proof of a result of Kuz'mina and Labbi concerning the Euler-Lagrange equations of the Gauss-Bonnet integral, and to give a new derivation of the Euh-Park-Sekigawa identity.Comment: 11 page

Eta invariants with spectral boundary conditions

We study the asymptotics of the heat trace \Tr\{fPe^{-tP^2}\} where $P$ is an operator of Dirac type, where $f$ is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary conditions. Using functorial techniques and special case calculations, the boundary part of the leading coefficients in the asymptotic expansion is found.Comment: 19 pages, LaTeX, extended Introductio

Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series

Let G be a compact Lie group acting transitively on Riemannian manifolds M and N. Let p be a G equivariant Riemannian submersion from M to N. We show that a smooth differential form on N has finite Fourier series if and only if the pull back has finite Fourier series on

Engine technology challenges for a 21st Century High-Speed Civil Transport

Ongoing NASA-funded studies by Boeing, McDonnell-Douglas, General Electric, and Pratt & Whitney indicate that an opportunity exists for a 21st Century High-Speed Civil Transport (HSCT) to become a major part of the international air transportation system. However, before industry will consider an HSCT product launch and an investment estimated to be over $15 billion for design and certification, major technology advances must be made. An overview of the propulsion-specific technology advances that must be in hand before an HSCT product launch could be considered is presented