Miscellaneous

• Smooth Limits of Piecewise Linear Approximations (with J. Barrett) J. Approx. Theory. 76 (1994) 107--122

  We consider particular types of discrete approximations to tensor fields on manifolds suggested by triangulations. The approximations are objects of finite geometrical extent, parameterized by a finite set of numbers, so they are suitable for numerical computations. We study the limiting behaviour of sequences of approximations and construct the theory so that the limits are tensor fields on the manifold. We propose a Cauchy criterion for our approximations which guarantees convergence to a limit. The specific examples include geodesic approximations to Riemannian and pseudoriemannian manifolds.

• Connections on Principal $S^1$-Bundles over Compacta (with L. Cordero and C. Dodson) Rev. Real Acad. Galega Cien. 13 (1994) 141--149

  The space of principal connections of principal circle bundles over $T^2$ and over $S^2$ is characterized. In particular, this latter includes the famous Hopf fibration.

• Hawking's Radiation via Fourier Integral Operators, in Geometry and Partial Differential Equations, ed. A. Prastaro and Th.M. Rassias. Singapore: World Scientific, 1994. pp.253--258

  This is a new geometric study in the theory of partial differential equations: an application of Fourier integral operators to equations with distributional coefficients. As an example, a derivation of the existence and spectrum of Hawking's radiation from a collapsing star is given.

• Compatible Metrics on Fiber Bundles, in Differential Geometry and Mathematical Physics, Contemp. Math. 170, eds. J.K. Beem and K.L. Duggal. Providence: A.M.S., 1994. pp.201--205

  We find all metric tensors on the total space of a fiber bundle which agree vertically with a given metric tensor on the model fiber and horizontally with one on the base space. We give some examples, and an application to Polyakov strings.

• Skewadjoint Operators on PseudoEuclidean Spaces (with C. Jang), preprint 29 Jan 03, 15pp. [also available as a PDF]

  We give a complete classification in canonical forms on finite-dimensional vector spaces over the real numbers.