Titlebook: Differential Geometry and Mathematical Physics; Lectures given at th M. Cahen,M. Wilde,L. Vanhecke Book 1983 D. Reidel Publishing Company,

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David Ben-Chaim,Yaffa Keret,Bat-Sheva IlanyLet (M,g) be an n-dimensional Riemannian manifold of class C. and let P be a q-dimensional submanifold of M. A (solid) tube of radius r about P is the set.where T.(P) denotes the normal space of P at the point m. For small r the set.is a smooth hypersurface which we also call a tube.

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Heat, Cold and GeometryClassical and relativistic mechanics can be formulated in terms of symplectic geometry; this formulation leads to a rigorous statement of the principles of statistical mechanics and of thermodynamics.

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Differential Deformations with Constant CoefficientsLet W be ?. and E(W,λ) be the space of formal series with coefficients in C. (W). A formal bi-differential operator P. is a bilinear map . with . where . is a usual bi-differential operator.

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Some Aspects of Theoretical Physics Relating to Harmonic MapsLet (M,g) be a compact Riemannian manifold without boundary, and consider an action which, for simplicity, we suppose has the form., where Φ is a section of a Riemannian fiber bundle π: E → M, and L: J. (E) → . possibly depends on the metric of E.

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